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prover.7.scm
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prover.7.scm
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(load "prover-load-j-bob.scm")
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A A 1) (ctx? x))
((A A 1) (if-nest-A (atom x) (equal x '?) (if (ctx? (car x)) 't (ctx? (cdr x)))))
((A Q) (ctx? x))
((A Q) (if-nest-A (atom x) (equal x '?) (if (ctx? (car x)) 't (ctx? (cdr x)))))
;; ((A A 1 1) (equal-if x '?))
;; ((A A 1) (equal-same '?))
;; ((A A) (equal-same 't))
;; ((A) (if-same (equal x '?) 't))
;; ((E A A A 1) (ctx? x))
;; ((E A A A 1)
;; (if-nest-E (atom x) (equal x '?) (if (ctx? (car x)) 't (ctx? (cdr x)))))
;; ((E)
;; (if-same (ctx? (car x))
;; (if (if (ctx? (car x)) (equal (ctx? (car x)) 't) 't)
;; (if (if (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't)
;; (if (ctx? x) (equal (if (ctx? (car x)) 't (ctx? (cdr x))) 't) 't)
;; 't)
;; 't)))
;; ((E A Q) (if-nest-A (ctx? (car x)) (equal (ctx? (car x)) 't) 't))
;; ((E A A A A 1) (if-nest-A (ctx? (car x)) 't (ctx? (cdr x))))
;; ((E E Q) (if-nest-E (ctx? (car x)) (equal (ctx? (car x)) 't) 't))
;; ((E E A A A 1) (if-nest-E (ctx? (car x)) 't (ctx? (cdr x))))
;; ((E A A A A) (equal-same 't))
;; ((E E)
;; (if-true
;; (if (if (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't)
;; (if (ctx? x) (equal (ctx? (cdr x)) 't) 't)
;; 't)
;; 't))
;; ((E A A A) (if-same (ctx? x) 't))
;; ((E A A) (if-same (if (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't) 't))
;; ((E A) (if-same (equal (ctx? (car x)) 't) 't))
;; ((E E A Q) (ctx? x))
;; ((E E A Q)
;; (if-nest-E (atom x) (equal x '?) (if (ctx? (car x)) 't (ctx? (cdr x)))))
;; ((E E A Q) (if-nest-E (ctx? (car x)) 't (ctx? (cdr x))))
;; ((E E)
;; (if-same (ctx? (cdr x))
;; (if (if (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't)
;; (if (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't)
;; 't)))
;; ((E E A Q)(if-nest-A (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't))
;; ((E E A A)(if-nest-A (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't))
;; ((E E E Q)(if-nest-E (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't))
;; ((E E E A)(if-nest-E (ctx? (cdr x)) (equal (ctx? (cdr x)) 't) 't))
;; ((E E E) (if-same 't 't))
;; ((E E A A 1) (equal-if (ctx? (cdr x)) 't))
;; ((E E A A) (equal-same 't))
;; ((E E A) (if-same (equal (ctx? (cdr x)) 't) 't))
((E E) (if-same (ctx? (cdr x)) 't))
((E) (if-same (ctx? (car x)) 't))
(() (if-same (atom x) 't)))
((dethm ctx?/sub (x y)
(if (ctx? x) (if (ctx? y) (equal (ctx? (sub x y)) 't) 't) 't))
(star-induction y)
(()
(if-same (ctx? x)
(if (atom y)
(if (ctx? x) (if (ctx? y) (equal (ctx? (sub x y)) 't) 't) 't)
(if (if (ctx? x)
(if (ctx? (car y)) (equal (ctx? (sub x (car y))) 't) 't)
't)
(if (if (ctx? x)
(if (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't)
't)
(if (ctx? x) (if (ctx? y) (equal (ctx? (sub x y)) 't) 't) 't)
't)
't))))
((A A) (if-nest-A (ctx? x) (if (ctx? y) (equal (ctx? (sub x y)) 't) 't) 't))
((A E Q)
(if-nest-A (ctx? x) (if (ctx? (car y)) (equal (ctx? (sub x (car y))) 't) 't) 't))
((A E A Q)
(if-nest-A (ctx? x) (if (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't) 't))
((A E A A) (if-nest-A (ctx? x) (if (ctx? y) (equal (ctx? (sub x y)) 't) 't) 't))
((E A) (if-nest-E (ctx? x) (if (ctx? y) (equal (ctx? (sub x y)) 't) 't) 't))
((E E Q)
(if-nest-E (ctx? x) (if (ctx? (car y)) (equal (ctx? (sub x (car y))) 't) 't) 't))
((E E A Q)
(if-nest-E (ctx? x) (if (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't) 't))
((E E A A) (if-nest-E (ctx? x) (if (ctx? y) (equal (ctx? (sub x y)) 't) 't) 't))
((E E A) (if-same 't 't))
((E E) (if-same 't 't))
((E) (if-same (atom y) 't))
((A A A 1 1) (sub x y))
((A A A 1 1)
(if-nest-A (atom y)
(if (equal y '?) x y)
(cons (sub x (car y)) (sub x (cdr y)))))
((A A A) (if-same (equal y '?) (equal (ctx? (if (equal y '?) x y)) 't)))
((A A A A 1 1) (if-nest-A (equal y '?) x y))
((A A A E 1 1) (if-nest-E (equal y '?) x y))
((A A A A 1) (ctx?/t x))
((A A A A) (equal-same 't))
((A A A E 1) (ctx?/t y))
((A A A E) (equal-same 't))
((A A A) (if-same (equal y '?) 't))
((A A) (if-same (ctx? y) 't))
((A E A A A 1 1) (sub x y))
((A E A A A 1 1)
(if-nest-E (atom y)
(if (equal y '?) x y)
(cons (sub x (car y)) (sub x (cdr y)))))
((A E A A A 1) (ctx? (cons (sub x (car y)) (sub x (cdr y)))))
((A E A A A 1 Q) (atom/cons (sub x (car y)) (sub x (cdr y))))
((A E A A A 1 E Q 1) (car/cons (sub x (car y)) (sub x (cdr y))))
((A E A A A 1 E E 1) (cdr/cons (sub x (car y)) (sub x (cdr y))))
((A E A A A 1)
(if-false (equal (cons (sub x (car y)) (sub x (cdr y))) '?)
(if (ctx? (sub x (car y))) 't (ctx? (sub x (cdr y))))))
((A E A A Q) (ctx? y))
((A E A A Q)
(if-nest-E (atom y) (equal y '?) (if (ctx? (car y)) 't (ctx? (cdr y)))))
((A E)
(if-same (ctx? (car y))
(if (if (ctx? (car y)) (equal (ctx? (sub x (car y))) 't) 't)
(if (if (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't)
(if (if (ctx? (car y)) 't (ctx? (cdr y)))
(equal (if (ctx? (sub x (car y))) 't (ctx? (sub x (cdr y)))) 't)
't)
't)
't)))
((A E A Q) (if-nest-A (ctx? (car y)) (equal (ctx? (sub x (car y))) 't) 't))
((A E A A A Q) (if-nest-A (ctx? (car y)) 't (ctx? (cdr y))))
((A E E Q) (if-nest-E (ctx? (car y)) (equal (ctx? (sub x (car y))) 't) 't))
((A E E A A Q) (if-nest-E (ctx? (car y)) 't (ctx? (cdr y))))
((A E A A A)
(if-true (equal (if (ctx? (sub x (car y))) 't (ctx? (sub x (cdr y)))) 't) 't))
((A E E)
(if-true
(if (if (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't)
(if (ctx? (cdr y))
(equal (if (ctx? (sub x (car y))) 't (ctx? (sub x (cdr y)))) 't)
't)
't)
't))
((A E A A A 1 Q) (equal-if (ctx? (sub x (car y))) 't))
((A E A A A 1) (if-true 't (ctx? (sub x (cdr y)))))
((A E A A A) (equal-same 't))
((A E A A) (if-same (if (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't) 't))
((A E A) (if-same (equal (ctx? (sub x (car y))) 't) 't))
((A E E)
(if-same (ctx? (cdr y))
(if (if (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't)
(if (ctx? (cdr y))
(equal (if (ctx? (sub x (car y))) 't (ctx? (sub x (cdr y)))) 't)
't)
't)))
((A E E A Q) (if-nest-A (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't))
((A E E A A)
(if-nest-A (ctx? (cdr y))
(equal (if (ctx? (sub x (car y))) 't (ctx? (sub x (cdr y)))) 't)
't))
((A E E E Q) (if-nest-E (ctx? (cdr y)) (equal (ctx? (sub x (cdr y))) 't) 't))
((A E E E A)
(if-nest-E (ctx? (cdr y))
(equal (if (ctx? (sub x (car y))) 't (ctx? (sub x (cdr y)))) 't)
't))
((A E E E) (if-same 't 't))
((A E E A A 1 E) (equal-if (ctx? (sub x (cdr y))) 't))
((A E E A A 1) (if-same (ctx? (sub x (car y))) 't))
((A E E A A) (equal-same 't))
((A E E A) (if-same (equal (ctx? (sub x (cdr y))) 't) 't))
((A E E) (if-same (ctx? (cdr y)) 't))
((A E) (if-same (ctx? (car y)) 't))
((A) (if-same (atom y) 't))
(() (if-same (ctx? x) 't)))))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E A A A 1) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E A A A 1) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E) (if-same (ctx? (car x))
(if (if (ctx? (car x))
(equal (ctx? (car x)) 't)
't)
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (if (ctx? (car x))
't
(ctx? (cdr x)))
(equal (if (ctx? (car x)) 't (ctx? (cdr x))) 't)
't)
't)
't)))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E A A A 1) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E) (if-same (ctx? (car x))
(if (if (ctx? (car x))
(equal (ctx? (car x)) 't)
't)
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (if (ctx? (car x))
't
(ctx? (cdr x)))
(equal (if (ctx? (car x)) 't (ctx? (cdr x))) 't)
't)
't)
't)))
((E A Q) (if-nest-A (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E A A A Q) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E A A A A 1) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E E Q) (if-nest-E (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E E A A Q) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A A A 1) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E A A A 1) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E) (if-same (ctx? (car x))
(if (if (ctx? (car x))
(equal (ctx? (car x)) 't)
't)
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (if (ctx? (car x))
't
(ctx? (cdr x)))
(equal (if (ctx? (car x)) 't (ctx? (cdr x))) 't)
't)
't)
't)))
((E A Q) (if-nest-A (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E A A A Q) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E A A A A 1) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E E Q) (if-nest-E (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E E A A Q) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A A A 1) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A) (if-same (ctx? (cdr x))
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
't)))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E A A A 1) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E) (if-same (ctx? (car x))
(if (if (ctx? (car x))
(equal (ctx? (car x)) 't)
't)
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (if (ctx? (car x))
't
(ctx? (cdr x)))
(equal (if (ctx? (car x)) 't (ctx? (cdr x))) 't)
't)
't)
't)))
((E A Q) (if-nest-A (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E A A A Q) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E A A A A 1) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E E Q) (if-nest-E (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E E A A Q) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A A A 1) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A) (if-same (ctx? (cdr x))
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
't)))
((E E A A Q) (if-nest-A (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A A A) (if-nest-A (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A E Q) (if-nest-E (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A E A) (if-nest-E (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)))))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E A A A 1) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E) (if-same (ctx? (car x))
(if (if (ctx? (car x))
(equal (ctx? (car x)) 't)
't)
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (if (ctx? (car x))
't
(ctx? (cdr x)))
(equal (if (ctx? (car x)) 't (ctx? (cdr x))) 't)
't)
't)
't)))
((E A Q) (if-nest-A (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E A A A Q) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E A A A A 1) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E E Q) (if-nest-E (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E E A A Q) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A A A 1) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A) (if-same (ctx? (cdr x))
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
't)))
((E E A A Q) (if-nest-A (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A A A) (if-nest-A (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A E Q) (if-nest-E (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A E A) (if-nest-E (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A A A 1) (equal-if (ctx? (cdr x)) 't))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E A A A 1) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((E) (if-same (ctx? (car x))
(if (if (ctx? (car x))
(equal (ctx? (car x)) 't)
't)
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (if (ctx? (car x))
't
(ctx? (cdr x)))
(equal (if (ctx? (car x)) 't (ctx? (cdr x))) 't)
't)
't)
't)))
((E A Q) (if-nest-A (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E A A A Q) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E A A A A 1) (if-nest-A (ctx? (car x))
't
(ctx? (cdr x))))
((E E Q) (if-nest-E (ctx? (car x))
(equal (ctx? (car x)) 't)
't))
((E E A A Q) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A A A 1) (if-nest-E (ctx? (car x))
't
(ctx? (cdr x))))
((E E A) (if-same (ctx? (cdr x))
(if (if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
(if (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't)
't)))
((E E A A Q) (if-nest-A (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A A A) (if-nest-A (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A E Q) (if-nest-E (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A E A) (if-nest-E (ctx? (cdr x))
(equal (ctx? (cdr x)) 't)
't))
((E E A A A 1) (equal-if (ctx? (cdr x)) 't))
((E E A A A) (equal-same 't))
)))
(jbob.prove (defun.ctx?)
'(((dethm ctx?/t (x)
(if (ctx? x) (equal (ctx? x) 't) 't))
(star-induction x)
((A Q) (ctx? x))
((A A 1) (ctx? x))
((A Q) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1) (if-nest-A (atom x)
(equal x '?)
(if (ctx? (car x))
't
(ctx? (cdr x)))))
((A A 1 1) (equal-if x '?))
((A A 1) (equal-same '?))
((A A) (equal-same 't))
((A) (if-same (equal x '?)
't))
((E A A Q) (ctx? x))
((E A A A 1) (ctx? x))
((E A A Q) (if-nest-E (atom x)
(equal x '?)
(if (ctx? (car x))