Nuprl Lemma : set-image_wf
∀[b:coSet{i:l}]. ∀[f:(x:coSet{i:l} × (x ∈ b)) ⟶ coSet{i:l}]. (set-image(f;b) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
set-image: set-image(f;b),
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 :
Wsup: Wsup(a;b),
mk-set: f"(T),
prop: ℙ,
subtype_rel: A ⊆r B,
mk-coset: mk-coset(T;f),
set-image: set-image(f;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtype_rel_self,
mem-mk-set_wf2,
setmem_wf,
coSet_wf,
mk-coset_wf,
coSet_subtype,
subtype_coSet
Rules used in proof :
isect_memberEquality,
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_pairEquality,
universeEquality,
because_Cache,
productEquality,
functionExtensionality,
lambdaEquality,
cumulativity,
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\}]. (set-image(f;b) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_08_45
Last ObjectModification:
2018_07_18-PM-00_32_38
Theory : constructive!set!theory
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