Theorems · Theorem · group theory
Set.forall_inv_mem
∀ {α : Type u_2} [inst : InvolutiveInv α] {s : Set α} {p : α → Prop}, (∀ (x : α), x⁻¹ ∈ s → p x) ↔ ∀ x ∈ s, p x⁻¹- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- InvolutiveInv
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- inv_invproof · cited by 494
- InvolutiveInvstatement and proof · cited by 102
- Equiv.forall_congr_rightproof · cited by 28
- Equiv.invproof · cited by 23
- Equiv.inv_applyproof · cited by 11
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