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prover.3.scm
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prover.3.scm
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(load "prover-load-j-bob.scm")
(jbob.step (defun.pair)
'(pair 'sharp 'cheddar)
'((() (pair 'sharp 'cheddar))))
(jbob.step (defun.second-of)
'(pair 'sharp 'cheddar)
'((() (pair 'sharp 'cheddar))))
(jbob.step (prelude)
'(pair 'sharp 'cheddar)
'((() (pair 'sharp 'cheddar))))
(jbob.prove (defun.second-of)
'(((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
;;((1) (first-of (cons a (cons b '()))))
)))
(jbob.prove (defun.second-of)
'(((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
((1) (first-of (cons a (cons b '()))))
)))
(jbob.prove (defun.second-of)
'(((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
((1) (first-of (cons a (cons b '()))))
((1) (car/cons a (cons b '()))))))
(jbob.prove (defun.second-of)
'(((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
((1) (first-of (cons a (cons b '()))))
((1) (car/cons a (cons b '())))
(() (equal-same a)))))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
;; ((1 1) (pair a '?))
;; ((1) (in-pair? (cons a (cons '? '()))))
;; ((1 Q 1) (first-of (cons a (cons '? '()))))
;; ((1 Q 1) (car/cons a (cons '? '())))
;; ((1 E 1) (second-of (cons a (cons '? '()))))
;; ((1 E 1 1) (cdr/cons a (cons '? '())))
;; ((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
;; ((1) (in-pair? (cons a (cons '? '()))))
;; ((1 Q 1) (first-of (cons a (cons '? '()))))
;; ((1 Q 1) (car/cons a (cons '? '())))
;; ((1 E 1) (second-of (cons a (cons '? '()))))
;; ((1 E 1 1) (cdr/cons a (cons '? '())))
;; ((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
;; ((1 Q 1) (first-of (cons a (cons '? '()))))
;; ((1 Q 1) (car/cons a (cons '? '())))
;; ((1 E 1) (second-of (cons a (cons '? '()))))
;; ((1 E 1 1) (cdr/cons a (cons '? '())))
;; ((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
;; ((1 Q 1) (car/cons a (cons '? '())))
;; ((1 E 1) (second-of (cons a (cons '? '()))))
;; ((1 E 1 1) (cdr/cons a (cons '? '())))
;; ((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
((1 Q 1) (car/cons a (cons '? '())))
;; ((1 E 1) (second-of (cons a (cons '? '()))))
;; ((1 E 1 1) (cdr/cons a (cons '? '())))
;; ((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
((1 Q 1) (car/cons a (cons '? '())))
((1 E 1) (second-of (cons a (cons '? '()))))
;; ((1 E 1 1) (cdr/cons a (cons '? '())))
;; ((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
((1 Q 1) (car/cons a (cons '? '())))
((1 E 1) (second-of (cons a (cons '? '()))))
((1 E 1 1) (cdr/cons a (cons '? '())))
;; ((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
((1 Q 1) (car/cons a (cons '? '())))
((1 E 1) (second-of (cons a (cons '? '()))))
((1 E 1 1) (cdr/cons a (cons '? '())))
((1 E 1) (car/cons '? '()))
;; ((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
((1 Q 1) (car/cons a (cons '? '())))
((1 E 1) (second-of (cons a (cons '? '()))))
((1 E 1 1) (cdr/cons a (cons '? '())))
((1 E 1) (car/cons '? '()))
((1 E) (equal-same '?))
;; ((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
((1 Q 1) (car/cons a (cons '? '())))
((1 E 1) (second-of (cons a (cons '? '()))))
((1 E 1 1) (cdr/cons a (cons '? '())))
((1 E 1) (car/cons '? '()))
((1 E) (equal-same '?))
((1) (if-same (equal a '?) 't))
;; (() (equal-same 't))
)))
(jbob.prove (dethm.in-first-of-pair)
'(((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?)) 't))
nil
((1 1) (pair a '?))
((1) (in-pair? (cons a (cons '? '()))))
((1 Q 1) (first-of (cons a (cons '? '()))))
((1 Q 1) (car/cons a (cons '? '())))
((1 E 1) (second-of (cons a (cons '? '()))))
((1 E 1 1) (cdr/cons a (cons '? '())))
((1 E 1) (car/cons '? '()))
((1 E) (equal-same '?))
((1) (if-same (equal a '?) 't))
(() (equal-same 't))
)))