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Theorems · Theorem · logic and foundations

IsWellFounded.rank_lt_of_rel

∀ {α : Type u} {a b : α} {r : α → α → Prop} [hwf : IsWellFounded α r],
  r a b → IsWellFounded.rank r a < IsWellFounded.rank r b
Defined in
Mathlib.SetTheory.Ordinal.Rank
Cited by
4 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IsWellFounded
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WellFoundedLT.rank_strictMono · cited by 1WellFoundedLT.rank_strict…WellFoundedGT.rank_strictAnti · cited by 0WellFoundedGT.rank_strict…toWellOrderExtension_strictMono · cited by 0toWellOrderExtension_stri…IsWellFounded.exists_well_order_ge · cited by 0IsWellFounded.exists_well…Ordinal · cited by 1688OrdinalIsWellFounded · cited by 18IsWellFoundedIsWellFounded.rank · cited by 9IsWellFounded.rankIsWellFounded.apply · cited by 5IsWellFounded.applyAcc.rank_lt_of_rel · cited by 1Acc.rank_lt_of_relIsWellFounded.rank_lt_of_relCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.