Nuprl Lemma : relclosed-set_wf
∀[R:Set{i:l} ⟶ Set{i:l} ⟶ ℙ']. ∀[s:Set{i:l}]. (closed(x,a.R[x;a])s ∈ ℙ')
Proof
Definitions occuring in Statement :
relclosed-set: closed(x,a.R[x; a])s,
Set: Set{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
so_apply: x[s1;s2],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
relclosed-set: closed(x,a.R[x; a])s,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
setmem_wf,
setsubset_wf,
Set_wf,
all_wf
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesisEquality,
cumulativity,
functionEquality,
lambdaEquality,
hypothesis,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[R:Set\{i:l\} {}\mrightarrow{} Set\{i:l\} {}\mrightarrow{} \mBbbP{}']. \mforall{}[s:Set\{i:l\}]. (closed(x,a.R[x;a])s \mmember{} \mBbbP{}')
Date html generated:
2018_05_29-PM-01_53_21
Last ObjectModification:
2018_05_25-PM-05_20_55
Theory : constructive!set!theory
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