Theorems · Theorem · geometry

lineMap_lt_lineMap_iff_of_lt

∀ {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 b : E}
  {r r' : k} [PosSMulReflectLT k E], r < r' → ((AffineMap.lineMap a b) r < (AffineMap.lineMap a b) r' ↔ a < b)

Defined in

Mathlib.LinearAlgebra.AffineSpace.Ordered

Cited by

2 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderIsOrderedRingAddCommGroupPartialOrderIsOrderedAddMonoidModuleIsStrictOrderedModulePosSMulReflectLT