Theorems · Theorem · commutative algebra
map_rat_smul
∀ {M : Type u_1} {M₂ : Type u_2} [inst : AddCommGroup M] [inst_1 : AddCommGroup M₂] [_instM : Module ℚ M]
[_instM₂ : Module ℚ M₂] {F : Type u_3} [inst_2 : FunLike F M M₂] [AddMonoidHomClass F M M₂] (f : F) (c : ℚ) (x : M),
f (c • x) = c • f x- Defined in
- Mathlib.Algebra.Module.Rat
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- FunLikestatement and proof · cited by 2,560
- AddMonoidHomClassstatement and proof · cited by 252
- map_ratCast_smulproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- star_rat_smulproof · cited by 2
- IsNilpotent.map_expproof · cited by 2
- Module.End.commute_exp_left_of_commuteproof · cited by 1
- NumberField.mixedEmbedding.mem_rat_span_latticeBasisproof · cited by 1
- NumberField.canonicalEmbedding.mem_rat_span_latticeBasisproof · cited by 1