Nuprl Lemma : consistent-context-model-stable
∀Gamma,more:mFOL() List. ∀M:mfol-context-model().
(consistent-context-model(Gamma;M) ⇒ consistent-context-model(more @ Gamma;M))
Proof
Definitions occuring in Statement :
consistent-context-model: consistent-context-model(Gamma;M),
mfol-context-model: mfol-context-model(),
mFOL: mFOL(),
append: as @ bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
mfol-context-model: mfol-context-model(),
consistent-context-model: consistent-context-model(Gamma;M),
and: P ∧ Q,
l_all: (∀x∈L.P[x]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T
Lemmas referenced :
consistent-model-const-stable,
select_wf,
nat_wf,
int_seg_properties,
length_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf,
list_wf,
consistent-context-model_wf,
mfol-context-model_wf,
mFOL_wf,
consistent-model-fun-stable,
consistent-model-fun_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
promote_hyp,
cut,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
productEquality,
atomEquality,
because_Cache,
setElimination,
rename,
independent_isectElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
imageElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}Gamma,more:mFOL() List. \mforall{}M:mfol-context-model().
(consistent-context-model(Gamma;M) {}\mRightarrow{} consistent-context-model(more @ Gamma;M))
Date html generated:
2018_05_21-PM-10_41_35
Last ObjectModification:
2017_07_26-PM-06_42_44
Theory : minimal-first-order-logic
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