Theorems · Theorem · group theory

Monoid.CoprodI.Word.mem_equivPair_tail_iff

∀ {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 j : ι} {w : Monoid.CoprodI.Word M} (m : M i),
  ⟨i, m⟩ ∈ ((Monoid.CoprodI.Word.equivPair j) w).tail.toList ↔
    ⟨i, m⟩ ∈ w.toList.tail ∨ i ≠ j ∧ ∃ (h : w.toList ≠ []), w.toList.head h = ⟨i, m⟩

Defined in: Mathlib.GroupTheory.CoprodI
Cited by: 2 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid DecidableEq DecidableEq

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Cites15

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
Monoidstatement and proof · cited by 3,887
Monoid.CoprodI.Wordstatement and proof · cited by 55
Monoid.CoprodI.Word.toListstatement and proof · cited by 39
Monoid.CoprodI.Word.Pairstatement and proof · cited by 32
Monoid.CoprodI.Word.fstIdxproof · cited by 30
Monoid.CoprodI.Word.Pair.tailstatement and proof · cited by 29
Monoid.CoprodI.Word.equivPairstatement · cited by 18
Monoid.CoprodI.Word.consproof · cited by 12
Monoid.CoprodI.Word.emptyproof · cited by 12
Monoid.CoprodI.Word.rconsproof · cited by 10

Cited by2

Results whose statement or proof uses this declaration.

Monoid.CoprodI.Word.mem_of_mem_equivPair_tailproof · cited by 0
Monoid.CoprodI.Word.mem_smul_iffproof · cited by 0