diff paper/src/NatAddSym.agda.replaced @ 3:959f4b34d6f4

add final thesis
author soto
date Tue, 09 Feb 2021 18:44:53 +0900 (2021-02-09)
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/paper/src/NatAddSym.agda.replaced	Tue Feb 09 18:44:53 2021 +0900
@@ -0,0 +1,12 @@
+open import Relation.Binary.PropositionalEquality
+open import nat
+open import nat_add
+open @$\equiv$@-Reasoning
+
+module nat_add_sym where
+
+addSym : (n m : Nat) @$\rightarrow$@ n + m @$\equiv$@ m + n
+addSym O       O   = refl
+addSym O    (S m)  = cong S (addSym O m)
+addSym (S n)   O   = cong S (addSym n O) 
+addSym (S n) (S m) = {!!} -- 後述