Theorems · Theorem · order theory
pow_two_semiclosed
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] [MulRightMono α] {a : α}, 1 ≤ a ^ 2 → 1 ≤ a- Defined in
- Mathlib.Algebra.Order.Group.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
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.
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- MulRightMonostatement and proof · cited by 263
- inf_of_le_leftproof · cited by 186
- pow_twoproof · cited by 150
- inf_commproof · cited by 139
- inf_eq_rightproof · cited by 64
- inf_assocproof · cited by 53
- mul_eq_leftproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- one_le_mabsproof · cited by 11