Theorems · Theorem · order theory
two_inv_lt_one
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α], 2⁻¹ < 1- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- one_divproof · cited by 624
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- Eq.trans_ltproof · cited by 34
- one_half_lt_oneproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.FarFromTriangleFree.lt_oneproof · cited by 1
- midpoint_le_rightproof · cited by 0
- right_le_midpointproof · cited by 0