Nuprl Lemma : least-equiv-is-equiv
∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ]. EquivRel(A;x,y.least-equiv(A;R) x y)
Proof
Definitions occuring in Statement :
least-equiv: least-equiv(A;R),
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
istype-universe,
least-equiv-is-equiv-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
functionIsType,
universeIsType,
hypothesisEquality,
because_Cache,
universeEquality,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality_alt,
independent_isectElimination
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. EquivRel(A;x,y.least-equiv(A;R) x y)
Date html generated:
2019_10_15-AM-10_24_57
Last ObjectModification:
2019_08_22-AM-10_52_36
Theory : relations2
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