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Theorems · Theorem · general algebraic systems

Pi.mulSingle_eq_one_iff

∀ {ι : Type u_1} {M : ι → Type u_6} [inst : (i : ι) → One (M i)] [inst_1 : DecidableEq ι] {i : ι} {x : M i},
  Pi.mulSingle i x = 1 ↔ x = 1
Defined in
Mathlib.Algebra.Notation.Pi.Basic
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
OneDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Pi.mulSingle_ne_one_iff · cited by 1Pi.mulSingle_ne_one_iffRestrictedProduct.mulSingle_eq_one_iff · cited by 0RestrictedProduct.mulSing…Pi.mulSingle · cited by 111Pi.mulSinglePi.one_apply · cited by 22Pi.one_applyPi.mulSingle_eq_same · cited by 18Pi.mulSingle_eq_samePi.mulSingle_one · cited by 4Pi.mulSingle_onePi.mulSingle_eq_one_iffCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.