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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