Theorems · Theorem · group theory
Equiv.Perm.one_lt_card_support_of_ne_one
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {f : Equiv.Perm α}, f ≠ 1 → 1 < f.support.card- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
- Equiv.Perm.extproof · cited by 75
- Equiv.apply_eq_iff_eqproof · cited by 28
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.two_le_card_support_of_ne_oneproof · cited by 2
- Equiv.Perm.card_support_ne_oneproof · cited by 2
- Equiv.Perm.fixed_point_card_lt_of_ne_oneproof · cited by 1
- Matrix.isAddUnit_detp_smul_mul_adjpproof · cited by 0