Nuprl Lemma : ext-eq-equiv
EquivRel(Type;A,B.A ≡ B)
Proof
Definitions occuring in Statement :
equiv_rel: EquivRel(T;x,y.E[x; y]),
ext-eq: A ≡ B,
universe: Type
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
ext-eq_inversion,
ext-eq_wf,
ext-eq_transitivity,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaFormation_alt,
universeIsType,
universeEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
independent_isectElimination,
hypothesis,
inhabitedIsType
Latex:
EquivRel(Type;A,B.A \mequiv{} B)
Date html generated:
2020_05_20-AM-08_24_23
Last ObjectModification:
2018_10_12-PM-00_19_37
Theory : lattices
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