Nuprl Lemma : setmem-loopset
∀z:coSet{i:l}. ((z ∈ loopset()) ⇐⇒ seteq(z;loopset()))
Proof
Definitions occuring in Statement :
loopset: loopset(),
setmem: (x ∈ s),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
exists: ∃x:A. B[x],
top: Top,
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
it_wf,
setmem-mk-coset,
loopset-sq,
coSet_wf,
seteq_wf,
loopset_wf,
setmem_wf
Rules used in proof :
dependent_pairFormation,
productElimination,
voidEquality,
voidElimination,
isect_memberEquality,
sqequalRule,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}z:coSet\{i:l\}. ((z \mmember{} loopset()) \mLeftarrow{}{}\mRightarrow{} seteq(z;loopset()))
Date html generated:
2018_07_29-AM-09_52_02
Last ObjectModification:
2018_07_21-PM-00_12_44
Theory : constructive!set!theory
Home
Index