Nuprl Lemma : funclosed-set_wf
∀[f:Set{i:l} ⟶ Set{i:l}]. ∀[s:Set{i:l}]. (f-closed(s) ∈ ℙ')
Proof
Definitions occuring in Statement :
funclosed-set: f-closed(s),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
funclosed-set: f-closed(s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
setsubset_wf,
Set_wf,
all_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesisEquality,
functionEquality,
cumulativity,
lambdaEquality,
hypothesis,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[f:Set\{i:l\} {}\mrightarrow{} Set\{i:l\}]. \mforall{}[s:Set\{i:l\}]. (f-closed(s) \mmember{} \mBbbP{}')
Date html generated:
2018_05_29-PM-01_55_01
Last ObjectModification:
2018_05_25-AM-08_48_03
Theory : constructive!set!theory
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