lineMap_strict_mono_left
∀ {k : Type u_1} {E : Type u_2} [inst : Ring k] [inst_1 : PartialOrder k] [IsOrderedRing k] [inst_3 : AddCommGroup E]
[inst_4 : PartialOrder E] [IsOrderedAddMonoid E] [inst_6 : Module k E] [IsStrictOrderedModule k E] {a a' b : E}
{r : k}, a < a' → r < 1 → (AffineMap.lineMap a b) r < (AffineMap.lineMap a' b) r- Cited by
- 0 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.
Cites14
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
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- IsOrderedRingstatement and proof · cited by 777
- AffineMapstatement · cited by 674
- AffineMap.lineMapstatement · cited by 254
- sub_posproof · cited by 147
- IsStrictOrderedModulestatement and proof · cited by 111
- add_lt_add_leftproof · cited by 47
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