Theorems · Theorem · group theory

Monoid.CoprodI.Word.rcons_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} (p : Monoid.CoprodI.Word.Pair M i),
  Monoid.CoprodI.Word.rcons p = Monoid.CoprodI.of p.head • p.tail

Defined in: Mathlib.GroupTheory.CoprodI
Cited by: 3 results in Mathlib
Foundations: Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid DecidableEq DecidableEq

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Around this declaration

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

Cites15

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

DFunLike.coestatement and proof · 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 · cited by 55
Monoid.CoprodIstatement · cited by 52
Monoid.CoprodI.ofstatement · cited by 45
Monoid.CoprodI.Word.Pairstatement and proof · cited by 32
Monoid.CoprodI.Word.Pair.tailstatement and proof · cited by 29
Monoid.CoprodI.Word.Pair.headstatement and proof · cited by 22
Monoid.CoprodI.Word.equivPairproof · cited by 18
Monoid.CoprodI.Word.Pair.fstIdx_neproof · cited by 15

Cited by3

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
Monoid.CoprodI.Word.equivPair_head_smul_equivPair_tailproof · cited by 1