Nuprl Lemma : least-closed-set_wf
∀[B:Set{i:l}]. ∀[G:Set{i:l} ⟶ Set{i:l}]. (least-closed-set(B;G) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
least-closed-set: least-closed-set(B;G),
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,
least-closed-set: least-closed-set(B;G),
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
setunionfun_wf,
regext_wf,
itersetfun_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,
hypothesis,
lambdaEquality,
applyEquality,
setElimination,
rename,
setEquality,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[B:Set\{i:l\}]. \mforall{}[G:Set\{i:l\} {}\mrightarrow{} Set\{i:l\}]. (least-closed-set(B;G) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_09_41
Last ObjectModification:
2018_05_30-PM-04_30_22
Theory : constructive!set!theory
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