Nuprl Lemma : mFOL-abstract-has-value
∀[fmla:mFOL()]. (mFOL-abstract(fmla))↓
Proof
Definitions occuring in Statement :
mFOL-abstract: mFOL-abstract(fmla)
,
mFOL: mFOL()
,
has-value: (a)↓
,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
all: ∀x:A. B[x]
,
nat: ℕ
,
implies: P
⇒ Q
,
false: False
,
ge: i ≥ j
,
uimplies: b supposing a
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
not: ¬A
,
top: Top
,
and: P ∧ Q
,
prop: ℙ
,
guard: {T}
,
has-value: (a)↓
,
subtype_rel: A ⊆r B
,
int_seg: {i..j-}
,
lelt: i ≤ j < k
,
decidable: Dec(P)
,
or: P ∨ Q
,
le: A ≤ B
,
less_than': less_than'(a;b)
,
ext-eq: A ≡ B
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
sq_type: SQType(T)
,
eq_atom: x =a y
,
ifthenelse: if b then t else f fi
,
mFOatomic: name(vars)
,
mFOL_size: mFOL_size(p)
,
spreadn: spread3,
mFOL-abstract: mFOL-abstract(fmla)
,
mFOL_ind: mFOL_ind,
AbstractFOAtomic: AbstractFOAtomic(n;L)
,
bfalse: ff
,
bnot: ¬bb
,
assert: ↑b
,
mFOconnect: mFOconnect(knd;left;right)
,
cand: A c∧ B
,
less_than: a < b
,
squash: ↓T
,
FOConnective: FOConnective(knd)
,
mFOquant: mFOquant(isall;var;body)
,
FOQuantifier: FOQuantifier(isall)
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
le_wf,
mFOL_size_wf,
mFOL_wf,
int_seg_wf,
int_seg_properties,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
mFOL-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
has-value_wf_base,
is-exception_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
decidable__lt,
itermAdd_wf,
int_term_value_add_lemma,
lelt_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomSqleEquality,
applyEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
productElimination,
unionElimination,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
promote_hyp,
tokenEquality,
equalityElimination,
instantiate,
cumulativity,
atomEquality,
divergentSqle,
sqleReflexivity,
baseClosed,
imageElimination,
addEquality
Latex:
\mforall{}[fmla:mFOL()]. (mFOL-abstract(fmla))\mdownarrow{}
Date html generated:
2018_05_21-PM-10_22_32
Last ObjectModification:
2017_07_26-PM-06_38_13
Theory : minimal-first-order-logic
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