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feat(library/logic/axioms/examples/diaconescu): remove redundant hypothesis

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Leonardo de Moura 2015-04-16 14:04:09 -07:00
parent 7529ee0a5c
commit df8ebeeefc
1 changed files with 1 additions and 2 deletions
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library/logic/axioms/examples/diaconescu.lean
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@ -9,7 +9,6 @@ open eq.ops nonempty inhabited
-- Show that Excluded middle follows from -- Show that Excluded middle follows from
-- Hilbert's choice operator, function extensionality and Prop extensionality -- Hilbert's choice operator, function extensionality and Prop extensionality
context context
hypothesis propext {a b : Prop} : (a → b) → (b → a) → a = b
parameter p : Prop parameter p : Prop
private definition u [reducible] := epsilon (λx, x = true ∨ p) private definition u [reducible] := epsilon (λx, x = true ∨ p)
@ -40,7 +39,7 @@ assume Hp : p,
have Hr : (x = false ∨ p) → (x = true ∨ p), from have Hr : (x = false ∨ p) → (x = true ∨ p), from
assume A, or.inr Hp, assume A, or.inr Hp,
show (x = true ∨ p) = (x = false ∨ p), from show (x = true ∨ p) = (x = false ∨ p), from
propext Hl Hr), propext (iff.intro Hl Hr)),
show u = v, from show u = v, from
Hpred ▸ (eq.refl (epsilon (λ x, x = true ∨ p))) Hpred ▸ (eq.refl (epsilon (λ x, x = true ∨ p)))