Nuprl Lemma : MMTree-ext
∀[T:Type]. MMTree(T) ≡ lbl:Atom × if lbl =a "Leaf" then T if lbl =a "Node" then MMTree(T) List List else Void fi 
Proof
Definitions occuring in Statement : 
MMTree: MMTree(T)
, 
list: T List
, 
ifthenelse: if b then t else f fi 
, 
eq_atom: x =a y
, 
ext-eq: A ≡ B
, 
uall: ∀[x:A]. B[x]
, 
product: x:A × B[x]
, 
token: "$token"
, 
atom: Atom
, 
void: Void
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
ext-eq: A ≡ B
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
MMTree: MMTree(T)
, 
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
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
MMTreeco_size: MMTreeco_size(p)
, 
has-value: (a)↓
, 
so_lambda: λ2x.t[x]
, 
nequal: a ≠ b ∈ T 
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
decidable: Dec(P)
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
not: ¬A
, 
top: Top
, 
less_than: a < b
, 
squash: ↓T
, 
so_apply: x[s]
, 
nat: ℕ
, 
MMTree_size: MMTree_size(p)
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
Lemmas referenced : 
nat_properties, 
MMTree_size_wf, 
sum-nat, 
false_wf, 
add-nat, 
ifthenelse_wf, 
set-value-type, 
has-value_wf-partial, 
sum-partial-list-has-value, 
MMTree_wf, 
l_member_wf, 
subtype_rel_list, 
list-subtype, 
int-value-type, 
value-type-has-value, 
int_subtype_base, 
le_wf, 
set_subtype_base, 
nat_wf, 
subtype_partial_sqtype_base, 
length_wf, 
int_seg_wf, 
MMTreeco_size_wf, 
int_formula_prop_less_lemma, 
intformless_wf, 
decidable__lt, 
int_formula_prop_wf, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
int_seg_properties, 
select_wf, 
MMTreeco_wf, 
list_wf, 
length_wf_nat, 
sum-partial-nat, 
neg_assert_of_eq_atom, 
assert-bnot, 
bool_subtype_base, 
bool_cases_sqequal, 
equal_wf, 
eqff_to_assert, 
atom_subtype_base, 
subtype_base_sq, 
assert_of_eq_atom, 
eqtt_to_assert, 
bool_wf, 
eq_atom_wf, 
MMTreeco-ext
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
independent_pairFormation, 
lambdaEquality, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
cut, 
lemma_by_obid, 
hypothesis, 
isectElimination, 
hypothesisEquality, 
promote_hyp, 
productElimination, 
hypothesis_subsumption, 
applyEquality, 
sqequalRule, 
dependent_pairEquality, 
tokenEquality, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_isectElimination, 
because_Cache, 
instantiate, 
cumulativity, 
atomEquality, 
dependent_functionElimination, 
independent_functionElimination, 
dependent_pairFormation, 
voidElimination, 
callbyvalueAdd, 
baseClosed, 
natural_numberEquality, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidEquality, 
computeAll, 
imageElimination, 
introduction, 
equalityEquality, 
setEquality, 
dependent_set_memberEquality, 
universeEquality, 
sqleReflexivity, 
productEquality
Latex:
\mforall{}[T:Type]
    MMTree(T)  \mequiv{}  lbl:Atom  \mtimes{}  if  lbl  =a  "Leaf"  then  T
                                                  if  lbl  =a  "Node"  then  MMTree(T)  List  List
                                                  else  Void
                                                  fi 
Date html generated:
2016_05_16-AM-08_54_44
Last ObjectModification:
2016_01_17-AM-09_42_37
Theory : C-semantics
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