Nuprl Lemma : consistent-model-const-stable
∀Gamma,more:mFOL() List. ∀c:ℕ × Atom × ℕ × ℕ.
(consistent-model-const(Gamma;c) ⇒ consistent-model-const(more @ Gamma;c))
Proof
Definitions occuring in Statement :
consistent-model-const: consistent-model-const(Gamma;c),
mFOL: mFOL(),
append: as @ bs,
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
atom: Atom
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
consistent-model-const: consistent-model-const(Gamma;c),
spreadn: spread4,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
top: Top,
ge: i ≥ j ,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
let: let,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
cand: A c∧ B,
nequal: a ≠ b ∈ T ,
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
consistent-model-const_wf,
nat_wf,
list_wf,
mFOL_wf,
length-append,
non_neg_length,
nat_properties,
decidable__lt,
length_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
context-lookup-stable1,
lelt_wf,
context-lookup_wf,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
or_wf,
assert_wf,
mFOconnect?_wf,
not_wf,
equal-wf-T-base,
mFOconnect-knd_wf,
mFOquant?_wf,
mFOquant-isall_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
append_wf,
length_append,
subtype_rel_list,
top_wf,
less_than_wf,
mFOconnect-left_wf,
mFOconnect-right_wf,
FOL-subst_wf,
mFOquant-body_wf,
mFOquant-var_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_pairEquality,
hypothesis,
productEquality,
atomEquality,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
addEquality,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
dependent_set_memberEquality,
tokenEquality,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
applyEquality
Latex:
\mforall{}Gamma,more:mFOL() List. \mforall{}c:\mBbbN{} \mtimes{} Atom \mtimes{} \mBbbN{} \mtimes{} \mBbbN{}.
(consistent-model-const(Gamma;c) {}\mRightarrow{} consistent-model-const(more @ Gamma;c))
Date html generated:
2018_05_21-PM-10_41_15
Last ObjectModification:
2017_07_26-PM-06_42_34
Theory : minimal-first-order-logic
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