Theorems · Theorem · geometry

right_lt_lineMap_iff_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 : k}
  [PosSMulReflectLT k E], r < 1 → (b < (AffineMap.lineMap a b) r ↔ b < a)

Defined in

Mathlib.LinearAlgebra.AffineSpace.Ordered

Cited by

0 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderIsOrderedRingAddCommGroupPartialOrderIsOrderedAddMonoidModuleIsStrictOrderedModulePosSMulReflectLT