Nuprl Lemma : closure-set_wf
∀[B:Set{i:l}]. ∀[Y:Set{i:l} ⟶ Set{i:l}]. ∀[x:Set{i:l}]. (closure-set(B;Y;x) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
closure-set: closure-set(B;Y;x),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
closure-set: closure-set(B;Y;x),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
setunionfun_wf,
setimages_wf,
Set_wf,
setmem_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
setElimination,
rename,
hypothesis,
applyEquality,
setEquality,
cumulativity,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[B:Set\{i:l\}]. \mforall{}[Y:Set\{i:l\} {}\mrightarrow{} Set\{i:l\}]. \mforall{}[x:Set\{i:l\}]. (closure-set(B;Y;x) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_10_02
Last ObjectModification:
2018_05_30-PM-05_28_00
Theory : constructive!set!theory
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