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Theorems · Theorem · commutative algebra

AddSubmonoid.smul_induction_on

∀ {R : Type u_2} {A : Type u_3} [inst : AddMonoid R] [inst_1 : AddMonoid A] [inst_2 : DistribSMul R A]
  {M : AddSubmonoid R} {N : AddSubmonoid A} {C : A → Prop} {a : A},
  a ∈ M • N → (∀ m ∈ M, ∀ n ∈ N, C (m • n)) → (∀ (x y : A), C x → C y → C (x + y)) → C a
Defined in
Mathlib.Algebra.Ring.Submonoid.Pointwise
Cited by
2 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoidAddMonoidDistribSMul
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Around this declaration

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Submodule.smul_induction_on · cited by 10Submodule.smul_induction_…AddSubmonoid.mul_induction_on · cited by 0AddSubmonoid.mul_inductio…AddMonoid · cited by 2864AddMonoidAddSubmonoid · cited by 1178AddSubmonoidDistribSMul · cited by 117DistribSMulAddSubmonoid.smul · cited by 11AddSubmonoid.smulAddSubmonoid.smul_le · cited by 8AddSubmonoid.smul_leAddSubmonoid.smul_induction_onCITED BYCITES

Cites5

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Cited by2

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