Nuprl Lemma : consistent-model-fun-stable
∀Gamma,more:mFOL() List. ∀x:ℕ. ∀L:(ℕ × ℕ) List.
(consistent-model-fun(Gamma;x;L) ⇒ consistent-model-fun(more @ Gamma;x;L))
Proof
Definitions occuring in Statement :
consistent-model-fun: consistent-model-fun(Gamma;x;L),
mFOL: mFOL(),
append: as @ bs,
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
consistent-model-fun: consistent-model-fun(Gamma;x;L),
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
ge: i ≥ j ,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
le: A ≤ B,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
let: let,
cand: A c∧ B,
l_all: (∀x∈L.P[x]),
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
length-append,
non_neg_length,
mFOL_wf,
nat_properties,
decidable__lt,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
itermConstant_wf,
istype-int,
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,
decidable__le,
istype-le,
istype-less_than,
consistent-model-fun_wf,
list_wf,
nat_wf,
istype-nat,
select_wf,
int_seg_properties,
FOL-subst_wf,
mFOquant-body_wf,
context-lookup_wf,
mFOquant-var_wf,
int_seg_wf,
istype-assert,
mFOconnect?_wf,
istype-atom,
mFOconnect-knd_wf,
atom_subtype_base,
istype-void,
l_all_wf2,
less_than_wf,
append_wf,
equal_wf,
mFOconnect-left_wf,
mFOconnect-right_wf,
l_member_wf,
length_append,
subtype_rel_list,
top_wf,
mFOquant?_wf,
bool_wf,
mFOquant-isall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
isectElimination,
Error :memTop,
hypothesis,
hypothesisEquality,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
addEquality,
unionElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
universeIsType,
voidElimination,
dependent_set_memberEquality_alt,
productIsType,
productEquality,
inhabitedIsType,
inlFormation_alt,
closedConclusion,
imageElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
functionIsType,
applyEquality,
baseClosed,
sqequalBase,
spreadEquality,
setIsType,
inrFormation_alt
Latex:
\mforall{}Gamma,more:mFOL() List. \mforall{}x:\mBbbN{}. \mforall{}L:(\mBbbN{} \mtimes{} \mBbbN{}) List.
(consistent-model-fun(Gamma;x;L) {}\mRightarrow{} consistent-model-fun(more @ Gamma;x;L))
Date html generated:
2020_05_20-AM-09_12_06
Last ObjectModification:
2020_01_06-PM-04_59_55
Theory : minimal-first-order-logic
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