midpoint_le_midpoint
∀ {k : Type u_1} {E : Type u_2} [inst : Ring k] [inst_1 : LinearOrder k] [IsStrictOrderedRing k]
[inst_3 : AddCommGroup E] [inst_4 : PartialOrder E] [IsOrderedAddMonoid E] [inst_6 : Module k E]
[IsStrictOrderedModule k E] {a a' b b' : E} [inst_8 : Invertible 2],
a ≤ a' → b ≤ b' → midpoint k a b ≤ midpoint k a' b'- Cited by
- 2 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Invertiblestatement and proof · cited by 549
- midpointstatement · cited by 123
- IsStrictOrderedModulestatement and proof · cited by 111
- one_le_twoproof · cited by 44
- zero_le_twoproof · cited by 44
Cited by2
Results whose statement or proof uses this declaration.
- Urysohns.CU.approx_le_succproof · cited by 1
- Urysohns.CU.approx_mem_Icc_right_leftproof · cited by 1