Nuprl Lemma : onto-map_wf
∀[A,B:coSet{i:l}]. ∀[R:{u:coSet{i:l}| (u ∈ A)} ⟶ {v:coSet{i:l}| (v ∈ B)} ⟶ ℙ']. (R:(A ─>> B) ∈ ℙ')
Proof
Definitions occuring in Statement :
onto-map: R:(A ─>> B),
setmem: (x ∈ s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
onto-map: R:(A ─>> B),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtype_rel_self,
exists_wf,
setmem_wf,
coSet_wf,
all_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
setEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
universeEquality,
dependent_set_memberEquality,
applyEquality,
productEquality,
hypothesisEquality,
cumulativity,
functionEquality,
lambdaEquality,
hypothesis,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A,B:coSet\{i:l\}]. \mforall{}[R:\{u:coSet\{i:l\}| (u \mmember{} A)\} {}\mrightarrow{} \{v:coSet\{i:l\}| (v \mmember{} B)\} {}\mrightarrow{} \mBbbP{}'].
(R:(A {}>> B) \mmember{} \mBbbP{}')
Date html generated:
2018_07_29-AM-10_06_24
Last ObjectModification:
2018_07_20-PM-00_53_57
Theory : constructive!set!theory
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