Nuprl Lemma : coSet-mem-Set-implies-Set
∀[z:coSet{i:l}]. z ∈ Set{i:l} supposing ∃s:Set{i:l}. (z ∈ s)
Proof
Definitions occuring in Statement :
Set: Set{i:l},
setmem: (x ∈ s),
coSet: coSet{i:l},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
setmem_wf,
Set_wf,
exists_wf,
set-item_wf2,
coSet-seteq-Set,
set-subtype-coSet,
setmem-iff
Rules used in proof :
cumulativity,
lambdaEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
isectElimination,
independent_functionElimination,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
thin,
productElimination,
sqequalHypSubstitution,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[z:coSet\{i:l\}]. z \mmember{} Set\{i:l\} supposing \mexists{}s:Set\{i:l\}. (z \mmember{} s)
Date html generated:
2018_07_29-AM-09_51_43
Last ObjectModification:
2018_07_11-PM-02_39_06
Theory : constructive!set!theory
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