62 lines
1.6 KiB
Racket
62 lines
1.6 KiB
Racket
#lang s-exp "../redex-curnel.rkt"
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(require "sugar.rkt")
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;; TODO: Handle multiple provide forms properly
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;; TODO: Handle (all-defined-out) properly
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(provide
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true T
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thm:anything-implies-true
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false
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not
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and
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conj
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thm:and-is-symmetric proof:and-is-symmetric
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thm:proj1 proof:proj1
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thm:proj2 proof:proj2
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== refl)
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(data true : Type (T : true))
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(define-theorem thm:anything-implies-true (forall (P : Type) true))
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(qed thm:anything-implies-true (lambda (P : Type) T))
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(data false : Type)
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(define-type (not (A : Type)) (-> A false))
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(data and : (forall* (A : Type) (B : Type) Type)
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(conj : (forall* (A : Type) (B : Type)
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(x : A) (y : B) (and A B))))
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(define-theorem thm:and-is-symmetric
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(forall* (P : Type) (Q : Type) (ab : (and P Q)) (and Q P)))
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;; TODO: BAH! pattern matching on inductive families is still broken.
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(define proof:and-is-symmetric
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(lambda* (P : Type) (Q : Type) (ab : (and P Q))
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(case* ab
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((conj (P : Type) (Q : Type) (x : P) (y : Q)) (conj Q P y x)))))
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#;(qed thm:and-is-symmetric proof:and-is-symmetric)
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(define-theorem thm:proj1
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(forall* (A : Type) (B : Type) (c : (and A B)) A))
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(define proof:proj1
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(lambda* (A : Type) (B : Type) (c : (and A B))
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(case c (conj (lambda* (A : Type) (B : Type) (a : A) (b : B) a)))))
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(qed thm:proj1 proof:proj1)
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(define-theorem thm:proj2
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(forall* (A : Type) (B : Type) (c : (and A B)) B))
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(define proof:proj2
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(lambda* (A : Type) (B : Type) (c : (and A B))
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(case c (conj (lambda* (A : Type) (B : Type) (a : A) (b : B) b)))))
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(qed thm:proj2 proof:proj2)
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(data == : (forall* (A : Type) (x : A) (-> A Type))
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(refl : (forall* (A : Type) (x : A) (== A x x))))
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