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Theorems · Theorem · order theory

Pi.single_pos

∀ {ι : Type u_6} {α : ι → Type u_7} [inst : DecidableEq ι] [inst_1 : (i : ι) → Zero (α i)]
  [inst_2 : (i : ι) → Preorder (α i)] {i : ι} {a : α i}, 0 < Pi.single i a ↔ 0 < a
Defined in
Mathlib.Algebra.Order.Pi
Cited by
1 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqZeroPreorder
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Around this declaration

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

Function.locallyFinsuppWithin.single_pos · cited by 3locallyFinsuppWithin.sing…Preorder · cited by 7952PreorderPi.single · cited by 518Pi.singlelt_update_self_iff · cited by 2lt_update_self_iffPi.single_posCITED BYCITES

Cites3

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

Cited by1

Results whose statement or proof uses this declaration.