refactor(library/data/{list,set,finset}/basic.lean): make subset reserved notation

This commit is contained in:
Jeremy Avigad 2015-05-20 18:33:59 +10:00
parent fe32b9fa7f
commit 59c1801921
4 changed files with 4 additions and 3 deletions

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@ -453,7 +453,7 @@ quot.lift_on₂ s₁ s₂
(λ s₁ a i, mem_perm p₂ (s₁ a (mem_perm (perm.symm p₁) i))) (λ s₁ a i, mem_perm p₂ (s₁ a (mem_perm (perm.symm p₁) i)))
(λ s₂ a i, mem_perm (perm.symm p₂) (s₂ a (mem_perm p₁ i))))) (λ s₂ a i, mem_perm (perm.symm p₂) (s₂ a (mem_perm p₁ i)))))
infix `⊆`:50 := subset infix `⊆` := subset
theorem empty_subset (s : finset A) : ∅ ⊆ s := theorem empty_subset (s : finset A) : ∅ ⊆ s :=
quot.induction_on s (λ l, list.nil_sub (elt_of l)) quot.induction_on s (λ l, list.nil_sub (elt_of l))

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@ -286,7 +286,7 @@ assume nin nainl, absurd (or.inr nainl) nin
definition sublist (l₁ l₂ : list T) := ∀ ⦃a : T⦄, a ∈ l₁ → a ∈ l₂ definition sublist (l₁ l₂ : list T) := ∀ ⦃a : T⦄, a ∈ l₁ → a ∈ l₂
infix `⊆`:50 := sublist infix `⊆` := sublist
theorem nil_sub (l : list T) : [] ⊆ l := theorem nil_sub (l : list T) : [] ⊆ l :=
λ b i, false.elim (iff.mp (mem_nil_iff b) i) λ b i, false.elim (iff.mp (mem_nil_iff b) i)

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@ -22,7 +22,7 @@ theorem setext {a b : set X} (H : ∀x, x ∈ a ↔ x ∈ b) : a = b :=
funext (take x, propext (H x)) funext (take x, propext (H x))
definition subset (a b : set X) := ∀⦃x⦄, x ∈ a → x ∈ b definition subset (a b : set X) := ∀⦃x⦄, x ∈ a → x ∈ b
infix `⊆`:50 := subset infix `⊆` := subset
/- bounded quantification -/ /- bounded quantification -/

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@ -88,6 +88,7 @@ reserve infix `∈`:50
reserve infix `∉`:50 reserve infix `∉`:50
reserve infixl `∩`:70 reserve infixl `∩`:70
reserve infixl ``:65 reserve infixl ``:65
reserve infix `⊆`:50
/- other symbols -/ /- other symbols -/