Nuprl Lemma : seteq_equiv
EquivRel(coSet{i:l};s1,s2.seteq(s1;s2))
Proof
Definitions occuring in Statement :
seteq: seteq(s1;s2),
coSet: coSet{i:l},
equiv_rel: EquivRel(T;x,y.E[x; y])
Definitions unfolded in proof :
trans: Trans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
sym: Sym(T;x,y.E[x; y]),
cand: A c∧ B,
member: t ∈ T,
all: ∀x:A. B[x],
refl: Refl(T;x,y.E[x; y]),
and: P ∧ Q,
equiv_rel: EquivRel(T;x,y.E[x; y])
Lemmas referenced :
seteq_transitivity,
seteq_inversion,
seteq_weakening,
seteq_wf,
coSet_wf
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
because_Cache,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
introduction,
cut,
lambdaFormation,
independent_pairFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
EquivRel(coSet\{i:l\};s1,s2.seteq(s1;s2))
Date html generated:
2018_07_29-AM-09_51_24
Last ObjectModification:
2018_07_11-PM-00_17_16
Theory : constructive!set!theory
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