Theorems · Theorem · linear algebra

Module.Ray.ind

∀ (R : Type u_1) [inst : CommSemiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] {C : Module.Ray R M → Prop},
  (∀ (v : M) (hv : v ≠ 0), C (rayOfNeZero R v hv)) → ∀ (x : Module.Ray R M), C x

An induction principle for Module.Ray, used as induction x using Module.Ray.ind.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

10 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModule