Nuprl Lemma : consistent-model-const_wf
∀[Gamma:mFOL() List]. ∀[c:ℕ × Atom × ℕ × ℕ]. (consistent-model-const(Gamma;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
consistent-model-const: consistent-model-const(Gamma;c),
mFOL: mFOL(),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
product: x:A × B[x],
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
consistent-model-const: consistent-model-const(Gamma;c),
let: let,
spreadn: spread4,
prop: ℙ,
and: P ∧ Q,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
or: P ∨ Q,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
less_than_wf,
length_wf,
mFOL_wf,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
or_wf,
assert_wf,
mFOconnect?_wf,
context-lookup_wf,
lelt_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,
mFOconnect-left_wf,
mFOconnect-right_wf,
FOL-subst_wf,
mFOquant-body_wf,
mFOquant-var_wf,
true_wf,
nat_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productElimination,
thin,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
independent_isectElimination,
because_Cache,
dependent_set_memberEquality,
independent_pairFormation,
atomEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[Gamma:mFOL() List]. \mforall{}[c:\mBbbN{} \mtimes{} Atom \mtimes{} \mBbbN{} \mtimes{} \mBbbN{}]. (consistent-model-const(Gamma;c) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-10_41_07
Last ObjectModification:
2017_07_26-PM-06_42_31
Theory : minimal-first-order-logic
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