Nuprl Lemma : set-image_wf2
∀[b:coSet{i:l}]. ∀[f:(x:coSet{i:l} × (x ∈ b)) ⟶ Set{i:l}]. (set-image(f;b) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
set-image: set-image(f;b),
Set: Set{i:l},
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 :
so_apply: x[s],
prop: ℙ,
mk-coset: mk-coset(T;f),
Wsup: Wsup(a;b),
mk-set: f"(T),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
mkset: {f[t] | t ∈ T},
set-image: set-image(f;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
Set_wf,
coSet_wf,
mk-coset_wf,
setmem_wf,
subtype_rel_self,
mem-mk-set_wf2,
mkset_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{} Set\{i:l\}]. (set-image(f;b) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_08_49
Last ObjectModification:
2018_07_18-PM-00_36_16
Theory : constructive!set!theory
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