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Theorems · Theorem · combinatorics

Finset.Nonempty.forall_const

∀ {α : Type u_1} {s : Finset α}, s.Nonempty → ∀ {p : Prop}, (∀ x ∈ s, p) ↔ p
Defined in
Mathlib.Data.Finset.Empty
Cited by
3 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Finset.sup_const · cited by 5Finset.sup_constFinset.inf_const · cited by 1Finset.inf_constFinset.forall_mem_const · cited by 0Finset.forall_mem_constFinset · cited by 13712FinsetFinset.Nonempty · cited by 1001Finset.NonemptyNonempty.forall_constCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.