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Theorems · Theorem · logic and foundations

Relation.transGen_eq_self

∀ {α : Type u_1} {r : α → α → Prop} [IsTrans α r], Relation.TransGen r = r
Defined in
Mathlib.Logic.Relation
Cited by
8 results in Mathlib
Foundations
Depth 6 from the axioms · uses propext, Quot.sound
Assumes
IsTrans
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Quotient.mk_le_mk · cited by 2Quotient.mk_le_mkRelation.TransGen.lift' · cited by 1TransGen.lift'monotone_iff_forall_wcovBy · cited by 1monotone_iff_forall_wcovBystrictMono_iff_forall_covBy · cited by 1strictMono_iff_forall_cov…Relation.reflTransGen_eq_reflGen · cited by 0Relation.reflTransGen_eq_…Relation.reflTransGen_transGen · cited by 0Relation.reflTransGen_tra…Relation.transGen_minimal · cited by 0Relation.transGen_minimalRelation.transGen_idem · cited by 0Relation.transGen_idemIsTrans · cited by 157IsTransIsTrans.trans · cited by 22IsTrans.transRelation.transGen_eq_selfCITED BYCITES

Cites2

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

Cited by8

Results whose statement or proof uses this declaration.