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Theorems · Theorem · order theory

Prod.Lex.monotone_fst

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : LE β] (t c : Lex (α × β)),
  t ≤ c → (ofLex t).1 ≤ (ofLex c).1

See also monotone_fst_ofLex for a version stated in terms of Monotone.

Defined in
Mathlib.Data.Prod.Lex
Cited by
3 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
PreorderLE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.PartiallyWellOrderedOn.imageProdLex · cited by 1PartiallyWellOrderedOn.im…Prod.Lex.monotone_fst_ofLex · cited by 0Lex.monotone_fst_ofLexWCovBy.fst_ofLex · cited by 0WCovBy.fst_ofLexDFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivPreorder · cited by 7952PreorderLT.lt.le · cited by 2189lt.leEq.le · cited by 605Eq.leLex · cited by 370LexofLex · cited by 127ofLexProd.Lex.toLex_le_toLex · cited by 6Lex.toLex_le_toLexLex.monotone_fstCITED BYCITES

Cites8

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.