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Theorems · Theorem

Function.not_injective_iff

∀ {α : Sort u_1} {β : Sort u_2} {f : α → β}, ¬Function.Injective f ↔ ∃ a b, f a = f b ∧ a ≠ b
Defined in
Mathlib.Logic.Function.Basic
Cited by
6 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
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Matrix.PosDef.isUnit · cited by 4PosDef.isUnitOrdinalApprox.exists_lfpApprox_eq_lfpApprox · cited by 2OrdinalApprox.exists_lfpA…Function.not_injective_const · cited by 2Function.not_injective_co…Matrix.IsDetpBalanced.submatrix_of_card_le · cited by 1IsDetpBalanced.submatrix_…Matrix.detp_mul · cited by 1Matrix.detp_mulAffineIndependent.injective_affineSpan_image · cited by 0AffineIndependent.injecti…Function.not_injective_iffCITED BYCITES

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Nothing in Mathlib beyond the foundations.

Cited by6

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