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Theorems · Theorem · commutative algebra

Subsemiring.prod_mono

∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] ⦃s₁ s₂ : Subsemiring R⦄,
  s₁ ≤ s₂ → ∀ ⦃t₁ t₂ : Subsemiring S⦄, t₁ ≤ t₂ → s₁.prod t₁ ≤ s₂.prod t₂
Defined in
Mathlib.Algebra.Ring.Subsemiring.Basic
Cited by
2 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
NonAssocSemiringNonAssocSemiring
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Around this declaration

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Subsemiring.prod_mono_left · cited by 1Subsemiring.prod_mono_leftSubsemiring.prod_mono_right · cited by 1Subsemiring.prod_mono_rig…NonAssocSemiring · cited by 805NonAssocSemiringSubsemiring · cited by 456SubsemiringSet.prod_mono · cited by 52Set.prod_monoSubsemiring.prod · cited by 11Subsemiring.prodSubsemiring.prod_monoCITED BYCITES

Cites4

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Cited by2

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