mirror of https://github.com/nmvdw/HITs-Examples
17 lines
488 B
Plaintext
17 lines
488 B
Plaintext
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{-# OPTIONS --without-K --rewriting #-}
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open import HoTT
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open import Expressions
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module Thms where
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value : (e : Exp) -> Σ Nat (\n -> e == val n)
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value = Exp-ind
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(\e -> Σ Nat (\n -> e == val n))
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(\n -> n , idp)
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(\e₁ e₂ v₁ v₂ -> fst v₁ + fst v₂ ,
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(ap (\e -> plus e e₂) (snd v₁) ∙ ap (plus (val (fst v₁))) (snd v₂)) ∙ add (fst v₁) (fst v₂)
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)
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(\n m -> from-transp! (\e -> Σ Nat (\n -> e == val n)) (add n m) (pair= {!!} {!!}))
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(\e -> {!!})
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