Nuprl Lemma : isSet_functionality
∀a1,a2:coSet{i:l}. (seteq(a1;a2) ⇒ (isSet(a1) ⇐⇒ isSet(a2)))
Proof
Definitions occuring in Statement :
isSet: isSet(w),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
coSet: coSet{i:l},
seteq: seteq(s1;s2),
isSet: isSet(w)
Lemmas referenced :
coW-wfdd_functionality
Rules used in proof :
hypothesis,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
universeEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}a1,a2:coSet\{i:l\}. (seteq(a1;a2) {}\mRightarrow{} (isSet(a1) \mLeftarrow{}{}\mRightarrow{} isSet(a2)))
Date html generated:
2018_07_29-AM-09_50_39
Last ObjectModification:
2018_07_25-PM-03_40_36
Theory : constructive!set!theory
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