Theorems · Theorem · order theory
mul_eq_one_iff_of_one_le
∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : PartialOrder α] [MulLeftMono α] [MulRightMono α] {a b : α},
1 ≤ a → 1 ≤ b → (a * b = 1 ↔ a = 1 ∧ b = 1)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- mul_oneproof · cited by 3,885
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- MulOneClassstatement and proof · cited by 1,018
- MulLeftMonostatement and proof · cited by 410
- MulRightMonostatement and proof · cited by 263
- le_mul_of_le_of_one_leproof · cited by 4
- le_mul_of_one_le_of_leproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Finset.prod_eq_one_iff_of_one_le'proof · cited by 3
- Cardinal.isUnit_iffproof · cited by 1