Nuprl Lemma : fRuleexistsE-var_wf
∀[v:FOLRule()]. fRuleexistsE-var(v) ∈ ℤ supposing ↑fRuleexistsE?(v)
Proof
Definitions occuring in Statement : 
fRuleexistsE-var: fRuleexistsE-var(v)
, 
fRuleexistsE?: fRuleexistsE?(v)
, 
FOLRule: FOLRule()
, 
assert: ↑b
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
int: ℤ
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
ext-eq: A ≡ B
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
sq_type: SQType(T)
, 
guard: {T}
, 
eq_atom: x =a y
, 
ifthenelse: if b then t else f fi 
, 
fRuleexistsE?: fRuleexistsE?(v)
, 
pi1: fst(t)
, 
assert: ↑b
, 
bfalse: ff
, 
false: False
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
bnot: ¬bb
, 
fRuleexistsE-var: fRuleexistsE-var(v)
, 
pi2: snd(t)
Lemmas referenced : 
FOLRule-ext, 
eq_atom_wf, 
bool_wf, 
eqtt_to_assert, 
assert_of_eq_atom, 
subtype_base_sq, 
atom_subtype_base, 
unit_wf2, 
unit_subtype_base, 
it_wf, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_atom, 
assert_wf, 
fRuleexistsE?_wf, 
FOLRule_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
introduction, 
extract_by_obid, 
promote_hyp, 
sqequalHypSubstitution, 
productElimination, 
thin, 
hypothesis_subsumption, 
hypothesis, 
hypothesisEquality, 
applyEquality, 
sqequalRule, 
isectElimination, 
tokenEquality, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_isectElimination, 
instantiate, 
cumulativity, 
atomEquality, 
dependent_functionElimination, 
independent_functionElimination, 
because_Cache, 
voidElimination, 
dependent_pairFormation
Latex:
\mforall{}[v:FOLRule()].  fRuleexistsE-var(v)  \mmember{}  \mBbbZ{}  supposing  \muparrow{}fRuleexistsE?(v)
Date html generated:
2018_05_21-PM-10_29_01
Last ObjectModification:
2017_07_26-PM-06_41_16
Theory : minimal-first-order-logic
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