Nuprl Lemma : fun-graph_wf
∀[b:coSet{i:l}]. ∀[f:(x:coSet{i:l} × (x ∈ b)) ⟶ coSet{i:l}]. (fun-graph(b;f) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
fun-graph: fun-graph(b;f),
setmem: (x ∈ s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
prop: ℙ,
Wsup: Wsup(a;b),
mk-set: f"(T),
mk-coset: mk-coset(T;f),
subtype_rel: A ⊆r B,
fun-graph: fun-graph(b;f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
setmem_wf,
subtype_rel_self,
mem-mk-set_wf2,
orderedpairset_wf,
mk-coset_wf,
coSet_subtype,
subtype_coSet
Rules used in proof :
because_Cache,
isect_memberEquality,
cumulativity,
productEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_pairEquality,
lambdaEquality,
isectElimination,
thin,
productElimination,
sqequalHypSubstitution,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
hypothesis_subsumption,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[b:coSet\{i:l\}]. \mforall{}[f:(x:coSet\{i:l\} \mtimes{} (x \mmember{} b)) {}\mrightarrow{} coSet\{i:l\}]. (fun-graph(b;f) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_09_05
Last ObjectModification:
2018_07_18-PM-05_05_16
Theory : constructive!set!theory
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