Theorems · Theorem · order theory

Pi.Lex.sInf_apply_le

∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → CompleteLinearOrder (α i)]
  [inst_2 : WellFoundedLT ι] {s : Set (Lex ((i : ι) → (fun i => α i) i))} {i : ι}
  {e : Lex ((i : ι) → (fun i => α i) i)}, e ∈ s → (∀ j < i, e j = sInf s j) → sInf s i ≤ e i

Defined in

Mathlib.Order.CompleteLattice.PiLex

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderCompleteLinearOrderWellFoundedLT