Theorems · Theorem · commutative algebra
TensorProduct.one_smul
∀ {R : Type u_1} {R' : Type u_4} [inst : CommSemiring R] [inst_1 : Monoid R'] {M : Type u_7} {N : Type u_8}
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : DistribMulAction R' M] [inst_5 : Module R M]
[inst_6 : Module R N] [inst_7 : SMulCommClass R R' M] (x : TensorProduct R M N), 1 • x = x- Defined in
- Mathlib.LinearAlgebra.TensorProduct.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Monoidstatement and proof · cited by 3,887
- TensorProductstatement and proof · cited by 2,545
- SMulCommClassstatement and proof · cited by 1,927
- one_smulproof · cited by 1,374
- TensorProduct.tmulproof · cited by 1,182
- DistribMulActionstatement and proof · cited by 584
- TensorProduct.induction_onproof · cited by 81
- TensorProduct.smul_addproof · cited by 3
- TensorProduct.smul_zeroproof · cited by 3
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