Theorems · Theorem · commutative algebra
Subring.prod_bot_sup_bot_prod
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] (s : Subring R) (t : Subring S),
s.prod ⊥ ⊔ ⊥.prod t = s.prod t- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- le_antisymmproof · cited by 2,068
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- bot_leproof · cited by 306
- SetLike.mem_coeproof · cited by 302
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- MulMemClass.mul_memproof · cited by 173
- sup_leproof · cited by 159
- OneMemClass.one_memproof · cited by 87
- Subring.prodstatement and proof · cited by 11
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