Theorems · Theorem · group theory
AddSubmonoid.forall_mem_sup
∀ {N : Type u_4} [inst : AddCommMonoid N] {P : N → Prop} {s t : AddSubmonoid N},
(∀ x ∈ s ⊔ t, P x) ↔ ∀ x₁ ∈ s, ∀ x₂ ∈ t, P (x₁ + x₂)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.mem_supproof · cited by 8
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