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Theorems · Theorem · general algebraic systems

Pi.single_eq_zero_iff

∀ {ι : Type u_1} {M : ι → Type u_6} [inst : (i : ι) → Zero (M i)] [inst_1 : DecidableEq ι] {i : ι} {x : M i},
  Pi.single i x = 0 ↔ x = 0
Defined in
Mathlib.Algebra.Notation.Pi.Basic
Cited by
3 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ZeroDecidableEq
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Around this declaration

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

Pi.single_ne_zero_iff · cited by 2Pi.single_ne_zero_iffPiLp.single_eq_zero_iff · cited by 0PiLp.single_eq_zero_iffRestrictedProduct.single_eq_zero_iff · cited by 0RestrictedProduct.single_…Pi.single · cited by 518Pi.singlePi.single_eq_same · cited by 144Pi.single_eq_samePi.zero_apply · cited by 70Pi.zero_applyPi.single_zero · cited by 10Pi.single_zeroPi.single_eq_zero_iffCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.