Nuprl Lemma : set-item-mem
∀s:coSet{i:l}. ∀x:set-dom(s). (set-item(s;x) ∈ s)
Proof
Definitions occuring in Statement :
setmem: (x ∈ s),
set-item: set-item(s;x),
set-dom: set-dom(s),
coSet: coSet{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
refl: Refl(T;x,y.E[x; y]),
guard: {T},
equiv_rel: EquivRel(T;x,y.E[x; y]),
prop: ℙ,
exists: ∃x:A. B[x],
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
seteq-equiv,
coSet_wf,
set-dom_wf,
seteq_wf,
set-item_wf,
setmem-iff
Rules used in proof :
dependent_pairFormation,
independent_functionElimination,
productElimination,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}s:coSet\{i:l\}. \mforall{}x:set-dom(s). (set-item(s;x) \mmember{} s)
Date html generated:
2018_07_29-AM-09_50_03
Last ObjectModification:
2018_07_20-PM-05_45_52
Theory : constructive!set!theory
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