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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