Nuprl Lemma : RankEx4-ext
RankEx4() ≡ lbl:Atom × if lbl =a "Foo" then ℤ + RankEx4() else Void fi 
Proof
Definitions occuring in Statement : 
RankEx4: RankEx4()
, 
ifthenelse: if b then t else f fi 
, 
eq_atom: x =a y
, 
ext-eq: A ≡ B
, 
product: x:A × B[x]
, 
union: left + right
, 
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
, 
RankEx4: RankEx4()
, 
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
, 
RankEx4co_size: RankEx4co_size(p)
, 
has-value: (a)↓
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
prop: ℙ
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
RankEx4_size: RankEx4_size(p)
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
not: ¬A
Lemmas referenced : 
nat_properties, 
RankEx4_size_wf, 
false_wf, 
add-nat, 
RankEx4co_wf, 
subtype_rel_union, 
ifthenelse_wf, 
neg_assert_of_eq_atom, 
assert-bnot, 
bool_subtype_base, 
bool_cases_sqequal, 
equal_wf, 
eqff_to_assert, 
set-value-type, 
has-value_wf-partial, 
int-value-type, 
value-type-has-value, 
base_wf, 
le_wf, 
set_subtype_base, 
nat_wf, 
subtype_partial_sqtype_base, 
RankEx4co_size_wf, 
int_subtype_base, 
RankEx4_wf, 
atom_subtype_base, 
subtype_base_sq, 
assert_of_eq_atom, 
eqtt_to_assert, 
bool_wf, 
eq_atom_wf, 
RankEx4co-ext
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
independent_pairFormation, 
lambdaEquality, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
cut, 
lemma_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, 
inlEquality, 
inrEquality, 
dependent_set_memberEquality, 
natural_numberEquality, 
intEquality, 
baseApply, 
closedConclusion, 
baseClosed, 
equalityEquality, 
callbyvalueAdd, 
dependent_pairFormation, 
voidElimination, 
universeEquality, 
unionEquality, 
voidEquality, 
productEquality
Latex:
RankEx4()  \mequiv{}  lbl:Atom  \mtimes{}  if  lbl  =a  "Foo"  then  \mBbbZ{}  +  RankEx4()  else  Void  fi 
Date html generated:
2016_05_16-AM-09_04_02
Last ObjectModification:
2016_01_17-AM-09_41_40
Theory : C-semantics
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