Nuprl Lemma : co-seteq-iff
∀x,y:coSet{i:l}. (seteq(x;y) ⇐⇒ ∀z:coSet{i:l}. ((z ∈ x) ⇐⇒ (z ∈ y)))
Proof
Definitions occuring in Statement :
setmem: (x ∈ s),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
seteq: seteq(s1;s2),
coSet: coSet{i:l},
setmem: (x ∈ s),
so_apply: x[s],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW-equiv-iff
Rules used in proof :
hypothesis,
hypothesisEquality,
lambdaEquality,
sqequalRule,
dependent_functionElimination,
universeEquality,
thin,
isectElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}x,y:coSet\{i:l\}. (seteq(x;y) \mLeftarrow{}{}\mRightarrow{} \mforall{}z:coSet\{i:l\}. ((z \mmember{} x) \mLeftarrow{}{}\mRightarrow{} (z \mmember{} y)))
Date html generated:
2018_07_29-AM-09_50_05
Last ObjectModification:
2018_07_11-PM-00_39_34
Theory : constructive!set!theory
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