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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