Nuprl Lemma : mFOL-ext
mFOL() ≡ lbl:Atom × if lbl =a "atomic" then name:Atom × (ℤ List)
                    if lbl =a "connect" then knd:Atom × left:mFOL() × mFOL()
                    if lbl =a "quant" then isall:𝔹 × var:ℤ × mFOL()
                    else Void
                    fi 
Proof
Definitions occuring in Statement : 
mFOL: mFOL()
, 
list: T List
, 
ifthenelse: if b then t else f fi 
, 
eq_atom: x =a y
, 
bool: 𝔹
, 
ext-eq: A ≡ B
, 
product: x:A × B[x]
, 
int: ℤ
, 
token: "$token"
, 
atom: Atom
, 
void: Void
Definitions unfolded in proof : 
ext-eq: A ≡ B
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
mFOL: mFOL()
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
ifthenelse: if b then t else f fi 
, 
sq_type: SQType(T)
, 
guard: {T}
, 
eq_atom: x =a y
, 
mFOLco_size: mFOLco_size(p)
, 
has-value: (a)↓
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
spreadn: spread3, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
mFOL_size: mFOL_size(p)
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
not: ¬A
Lemmas referenced : 
mFOLco-ext, 
eq_atom_wf, 
bool_wf, 
eqtt_to_assert, 
assert_of_eq_atom, 
subtype_base_sq, 
atom_subtype_base, 
list_wf, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_atom, 
int_subtype_base, 
mFOLco_size_wf, 
subtype_partial_sqtype_base, 
nat_wf, 
set_subtype_base, 
le_wf, 
base_wf, 
value-type-has-value, 
int-value-type, 
has-value_wf-partial, 
set-value-type, 
mFOL_wf, 
ifthenelse_wf, 
mFOLco_wf, 
add-nat, 
false_wf, 
mFOL_size_wf, 
nat_properties
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
independent_pairFormation, 
lambdaEquality, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
cut, 
introduction, 
extract_by_obid, 
hypothesis, 
promote_hyp, 
productElimination, 
hypothesis_subsumption, 
hypothesisEquality, 
applyEquality, 
sqequalRule, 
dependent_pairEquality, 
isectElimination, 
tokenEquality, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_isectElimination, 
because_Cache, 
instantiate, 
cumulativity, 
atomEquality, 
dependent_functionElimination, 
independent_functionElimination, 
intEquality, 
dependent_pairFormation, 
voidElimination, 
dependent_set_memberEquality, 
natural_numberEquality, 
baseApply, 
closedConclusion, 
baseClosed, 
callbyvalueAdd, 
productEquality, 
universeEquality, 
voidEquality, 
sqleReflexivity
Latex:
mFOL()  \mequiv{}  lbl:Atom  \mtimes{}  if  lbl  =a  "atomic"  then  name:Atom  \mtimes{}  (\mBbbZ{}  List)
                                        if  lbl  =a  "connect"  then  knd:Atom  \mtimes{}  left:mFOL()  \mtimes{}  mFOL()
                                        if  lbl  =a  "quant"  then  isall:\mBbbB{}  \mtimes{}  var:\mBbbZ{}  \mtimes{}  mFOL()
                                        else  Void
                                        fi 
Date html generated:
2018_05_21-PM-10_20_50
Last ObjectModification:
2017_07_26-PM-06_37_37
Theory : minimal-first-order-logic
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