lineMap_le_lineMap_iff_of_lt
∀ {k : Type u_1} {E : Type u_2} [inst : Field 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] [PosSMulReflectLE k E] {a b : E} {r r' : k},
r < r' → ((AffineMap.lineMap a b) r ≤ (AffineMap.lineMap a b) r' ↔ a ≤ b)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- AffineMapstatement · cited by 674
- AffineMap.lineMapstatement · cited by 254
- sub_posproof · cited by 147
- IsStrictOrderedModulestatement and proof · cited by 111
Cited by2
Results whose statement or proof uses this declaration.
- left_le_lineMap_iff_leproof · cited by 2
- lineMap_le_right_iff_leproof · cited by 2