Theorems · Theorem · commutative algebra
Ideal.inf_ne_bot_of_ne_bot
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {I J : Ideal R} [I.IsTwoSided], I ≠ ⊥ → J ≠ ⊥ → I ⊓ J ≠ ⊥- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- le_reflproof · cited by 2,061
- NoZeroDivisorsstatement and proof · cited by 545
- Ideal.IsTwoSidedstatement and proof · cited by 179
- bot_lt_iff_ne_botproof · cited by 57
- lt_imp_lt_of_le_of_leproof · cited by 53
- Ideal.mul_le_infproof · cited by 10
- Ideal.mul_eq_botproof · cited by 3
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