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Theorems · Theorem · linear algebra

rayOfNeZero.congr_simp

∀ (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] (v v_1 : M) (e_v : v = v_1) (h : v ≠ 0),
  rayOfNeZero R v h = rayOfNeZero R v_1 ⋯
Defined in
Mathlib.LinearAlgebra.Ray
Cited by
4 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Module.Basis.orientation_map · cited by 3Basis.orientation_mapModule.Ray.map_neg · cited by 2Ray.map_negModule.Ray.neg_units_smul · cited by 2Ray.neg_units_smulModule.Basis.orientation_reindex · cited by 0Basis.orientation_reindexModule · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingModule.Ray · cited by 30Module.RayrayOfNeZero · cited by 22rayOfNeZerorayOfNeZero.congr_simpCITED BYCITES

Cites7

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Cited by4

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