Theorems · Theorem · group theory

Monoid.CoprodI.Word.cons_eq_smul

∀ {ι : Type u_1} {M : ι → Type u_2} [inst : (i : ι) → Monoid (M i)] [inst_1 : DecidableEq ι]
  [inst_2 : (i : ι) → DecidableEq (M i)] {i : ι} {m : M i} {ls : Monoid.CoprodI.Word M} {h1 : ls.fstIdx ≠ some i}
  {h2 : m ≠ 1}, Monoid.CoprodI.Word.cons m ls h1 h2 = Monoid.CoprodI.of m • ls

Defined in: Mathlib.GroupTheory.CoprodI
Cited by: 2 results in Mathlib
Foundations: Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid DecidableEq DecidableEq

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Cites18

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

DFunLike.coestatement · cited by 62,936
Monoidstatement and proof · cited by 3,887
mul_oneproof · cited by 3,885
MonoidHomstatement · cited by 3,629
Monoid.CoprodI.Wordstatement and proof · cited by 55
Monoid.CoprodIstatement · cited by 52
Monoid.CoprodI.ofstatement · cited by 45
Monoid.CoprodI.Word.toListproof · cited by 39
Monoid.CoprodI.Word.Pairproof · cited by 32
Monoid.CoprodI.Word.fstIdxstatement and proof · cited by 30
Monoid.CoprodI.Word.Pair.tailproof · cited by 29
Monoid.CoprodI.Word.Pair.headproof · cited by 22

Cited by2

Results whose statement or proof uses this declaration.

Monoid.PushoutI.NormalWord.cons_eq_smulproof · cited by 1
Monoid.CoprodI.Word.smul_inductionproof · cited by 0