Nuprl Lemma : FOConnective_wf
∀[vsa,vsb:ℤ List].
  ∀knd:Atom
    (FOConnective(knd) ∈ AbstractFOFormula(vsa)
     ⟶ AbstractFOFormula(vsb)
     ⟶ AbstractFOFormula(val-union(IntDeq;vsa;vsb)))
Proof
Definitions occuring in Statement : 
FOConnective: FOConnective(knd)
, 
AbstractFOFormula: AbstractFOFormula(vs)
, 
val-union: val-union(eq;as;bs)
, 
list: T List
, 
int-deq: IntDeq
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
int: ℤ
, 
atom: Atom
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
AbstractFOFormula: AbstractFOFormula(vs)
, 
FOConnective: FOConnective(knd)
, 
uimplies: b supposing a
, 
prop: ℙ
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
subtype_rel: A ⊆r B
, 
implies: P 
⇒ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
FOAssignment_wf, 
val-union_wf, 
int-deq_wf, 
int-valueall-type, 
FOStruct_wf, 
list_wf, 
union-contains, 
union-contains2, 
val-union-l-union, 
subtype_rel_FOAssignment, 
FOSatWith_wf, 
let_wf, 
ifthenelse_wf, 
eq_atom_wf, 
or_wf, 
equal_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaFormation, 
lambdaEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
intEquality, 
hypothesis, 
hypothesisEquality, 
independent_isectElimination, 
cumulativity, 
universeEquality, 
functionEquality, 
atomEquality, 
sqequalRule, 
dependent_functionElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
because_Cache, 
isect_memberEquality, 
independent_pairFormation, 
applyEquality, 
productElimination, 
instantiate, 
tokenEquality, 
productEquality, 
independent_functionElimination
Latex:
\mforall{}[vsa,vsb:\mBbbZ{}  List].
    \mforall{}knd:Atom
        (FOConnective(knd)  \mmember{}  AbstractFOFormula(vsa)
          {}\mrightarrow{}  AbstractFOFormula(vsb)
          {}\mrightarrow{}  AbstractFOFormula(val-union(IntDeq;vsa;vsb)))
Date html generated:
2018_05_21-PM-10_20_33
Last ObjectModification:
2017_07_26-PM-06_37_31
Theory : minimal-first-order-logic
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