Theorems · Theorem · group theory

Monoid.CoprodI.Word.equivPair_tail_eq_inv_smul

∀ {ι : Type u_1} [inst : DecidableEq ι] {G : ι → Type u_4} [inst_1 : (i : ι) → Group (G i)]
  [inst_2 : (i : ι) → DecidableEq (G i)] {i : ι} (w : Monoid.CoprodI.Word G),
  ((Monoid.CoprodI.Word.equivPair i) w).tail = (Monoid.CoprodI.of ((Monoid.CoprodI.Word.equivPair i) w).head)⁻¹ • w

Defined in: Mathlib.GroupTheory.CoprodI
Cited by: 2 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq Group DecidableEq

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Cites13

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

DFunLike.coestatement · cited by 62,936
Equivstatement · cited by 8,337
Groupstatement and proof · cited by 6,238
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.Pairstatement · cited by 32
Monoid.CoprodI.Word.Pair.tailstatement · cited by 29
Monoid.CoprodI.Word.Pair.headstatement · cited by 22
Monoid.CoprodI.Word.equivPairstatement · cited by 18
inv_smul_eq_iffproof · cited by 16

Cited by2

Results whose statement or proof uses this declaration.

Monoid.PushoutI.NormalWord.prod_summand_smulproof · cited by 1
Monoid.PushoutI.NormalWord.cons_eq_smulproof · cited by 1