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Theorems · Theorem · commutative algebra

Subring.prod_mono

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

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

Subring.prod_mono_left · cited by 1Subring.prod_mono_leftSubring.prod_mono_right · cited by 1Subring.prod_mono_rightSubring · cited by 602SubringNonAssocRing · cited by 483NonAssocRingSet.prod_mono · cited by 52Set.prod_monoSubring.prod · cited by 11Subring.prodSubring.prod_monoCITED BYCITES

Cites4

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Cited by2

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