Theorems · Theorem · group theory
SubmonoidClass.swap_mem_trans
∀ {α : Type u_2} [inst : DecidableEq α] {a b c : α} {C : Type u_3} [inst_1 : SetLike C (Equiv.Perm α)]
[SubmonoidClass C (Equiv.Perm α)] (M : C), Equiv.swap a b ∈ M → Equiv.swap b c ∈ M → Equiv.swap a c ∈ M- Defined in
- Mathlib.GroupTheory.Perm.ClosureSwap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.Permstatement and proof · cited by 1,375
- eq_or_neproof · cited by 1,117
- SetLikestatement and proof · cited by 1,084
- Equiv.swapstatement and proof · cited by 197
- MulMemClass.mul_memproof · cited by 173
- OneMemClass.one_memproof · cited by 87
- SubmonoidClassstatement and proof · cited by 60
- Equiv.swap_selfproof · cited by 18
- Equiv.swap_commproof · cited by 11
- Equiv.swap_mul_swap_mul_swapproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- swap_mem_closure_isSwapproof · cited by 1