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fix(library/data/finset/to_set.lean): to_set does not require decidable equality

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This commit is contained in:
Jeremy Avigad 2015-05-31 10:24:41 +10:00
parent 1238f43575
commit cdecc309b3
1 changed files with 3 additions and 2 deletions
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5
library/data/finset/to_set.lean
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@ -12,10 +12,9 @@ namespace finset
variable {A : Type}
variable [deceq : decidable_eq A]
include deceq
definition to_set (s : finset A) : set A := λx, x ∈ s
abbreviation ts := @to_set A _ -- until coercion is working
abbreviation ts := @to_set A
variables (s t : finset A) (x : A)
@ -28,6 +27,8 @@ theorem mem_to_set_univ [h : fintype A] : (x ∈ ts univ) = (x ∈ set.univ) :=
propext (iff.intro (assume H, trivial) (assume H, !mem_univ))
theorem to_set_univ [h : fintype A] : ts univ = (set.univ : set A) := funext (λ x, !mem_to_set_univ)
include deceq
theorem mem_to_set_union : (x ∈ ts (s ∪ t)) = (x ∈ ts s ∪ ts t) := !finset.mem_union_eq
theorem to_set_union : ts (s ∪ t) = ts s ∪ ts t := funext (λ x, !mem_to_set_union)