Nuprl Lemma : singlevalued-graph_wf
∀A:coSet{i:l}. ∀B:{a:coSet{i:l}| (a ∈ A)} ⟶ coSet{i:l}. ∀x:coSet{i:l}. (singlevalued-graph(A;a.B[a];x) ∈ ℙ)
Proof
Definitions occuring in Statement :
singlevalued-graph: singlevalued-graph(A;a.B[a];grph),
setmem: (x ∈ s),
coSet: coSet{i:l},
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
singlevalued-graph: singlevalued-graph(A;a.B[a];grph),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
seteq_wf,
orderedpairset_wf,
setmem_wf,
allsetmem_wf
Rules used in proof :
cumulativity,
setEquality,
because_Cache,
hypothesis,
rename,
setElimination,
functionEquality,
applyEquality,
lambdaEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}A:coSet\{i:l\}. \mforall{}B:\{a:coSet\{i:l\}| (a \mmember{} A)\} {}\mrightarrow{} coSet\{i:l\}. \mforall{}x:coSet\{i:l\}.
(singlevalued-graph(A;a.B[a];x) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-10_04_50
Last ObjectModification:
2018_07_18-PM-03_32_07
Theory : constructive!set!theory
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