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Theorems · Theorem · logic and foundations

Membership.mem.ne_of_notMem

∀ {α : Type u_1} {β : Type u_2} [inst : Membership α β] {s : β} {a b : α}, a ∈ s → b ∉ s → a ≠ b

Alias of ne_of_mem_of_not_mem.

Defined in
Mathlib.Logic.Basic
Cited by
4 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
Membership
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DFinsupp.Lex.acc_of_single · cited by 2Lex.acc_of_singleFinset.slice_union_shadow_falling_succ · cited by 1Finset.slice_union_shadow…SimpleGraph.induce_deleteIncidenceSet_of_notMem · cited by 1SimpleGraph.induce_delete…ArithmeticFunction.IsMultiplicative.map_prod · cited by 1IsMultiplicative.map_prodmem.ne_of_notMemCITED BYCITES

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Nothing in Mathlib beyond the foundations.

Cited by4

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