Nuprl Lemma : regextfun_wf
∀[T:Type]. ∀[f:T ⟶ coSet{i:l}]. ∀[w:coW(T;x.set-dom(f x))]. (regextfun(f;w) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
regextfun: regextfun(f;w),
set-dom: set-dom(s),
coSet: coSet{i:l},
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
ext-eq: A ≡ B,
Wsup: Wsup(a;b),
mk-set: f"(T),
regextfun: regextfun(f;w),
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x.t[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
subtype_rel_wf,
set_wf,
subtype_rel_weakening,
coW-ext,
set-dom_wf,
coW_wf,
fix_wf_coSet_system
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
instantiate,
universeEquality,
functionExtensionality,
rename,
setElimination,
dependent_pairEquality,
productElimination,
independent_isectElimination,
functionEquality,
productEquality,
because_Cache,
hypothesis_subsumption,
isect_memberEquality,
hypothesis,
applyEquality,
lambdaEquality,
sqequalRule,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} coSet\{i:l\}]. \mforall{}[w:coW(T;x.set-dom(f x))]. (regextfun(f;w) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_07_04
Last ObjectModification:
2018_07_20-PM-04_48_59
Theory : constructive!set!theory
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