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Rem extra args from identity (#49)

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Patrick Stevens
2019-10-03 07:21:30 +01:00
committed by GitHub
parent 7ed41b0c09
commit 5af4030361
14 changed files with 165 additions and 167 deletions
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4
Sets/FinSet.agda
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@@ -81,14 +81,14 @@ module Sets.FinSet where
finNotEqualsFsucc {.0} {a} {b} (fne2 .(fsucc a) .(fsucc b) (inr (() ,, snd)))
finNotEqualsFsucc {n} {a} {b} (fneN .(fsucc a) .(fsucc b) (inl (inl (() ,, snd))))
finNotEqualsFsucc {n} {a} {b} (fneN .(fsucc a) .(fsucc b) (inl (inr (fst ,, ()))))
finNotEqualsFsucc {n} {a} {b} (fneN .(fsucc a) .(fsucc b) (inr ((fst ,, snd) , prf))) = identityOfIndiscernablesRight _ _ _ FinNotEquals ans (equalityCommutative b=snd)
finNotEqualsFsucc {n} {a} {b} (fneN .(fsucc a) .(fsucc b) (inr ((fst ,, snd) , prf))) = identityOfIndiscernablesRight FinNotEquals ans (equalityCommutative b=snd)
where
a=fst : a ≡ fst
a=fst = fsuccInjective (_&_&_.one prf)
b=snd : b ≡ snd
b=snd = fsuccInjective (_&_&_.two prf)
ans : FinNotEquals a snd
ans = identityOfIndiscernablesLeft _ _ _ FinNotEquals (_&_&_.three prf) (equalityCommutative a=fst)
ans = identityOfIndiscernablesLeft FinNotEquals (_&_&_.three prf) (equalityCommutative a=fst)
finSetNotEquals' : {n : ℕ} → {a b : FinSet (succ n)} → FinNotEquals a b → (a ≡ b → False)
finSetNotEquals' {n} {a} {.a} fne refl = finSetNotEqualsSame fne