Nuprl Lemma : MMTree-rank_wf
∀T:Type. ∀t:MMTree(T). (MMTree-rank(t) ∈ ℕ)
Proof
Definitions occuring in Statement :
MMTree-rank: MMTree-rank(t),
MMTree: MMTree(T),
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
MMTree_Leaf: MMTree_Leaf(val),
MMTree_size: MMTree_size(p),
MMTree-rank: MMTree-rank(t),
MMTree_Leaf?: MMTree_Leaf?(v),
pi1: fst(t),
MMTree_Node-forest: MMTree_Node-forest(v),
pi2: snd(t),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
MMTree_Node: MMTree_Node(forest),
so_lambda: λ2x.t[x],
less_than: a < b,
squash: ↓T,
so_apply: x[s],
cand: A c∧ B,
nat_plus: ℕ+,
true: True,
l_member: (x ∈ l)
Lemmas referenced :
and_wf,
squash_wf,
add-is-int-iff,
nat_plus_properties,
nat_plus_wf,
add_nat_plus,
map-length,
length_of_cons_lemma,
cons_wf,
imax-list_wf,
map_wf,
imax-list-is-nat,
l_member_wf,
list-subtype,
nat_wf,
sum-nat-le,
sum-nat-less,
int_term_value_add_lemma,
itermAdd_wf,
length_wf,
decidable__lt,
select_wf,
MMTree_wf,
list_wf,
length_wf_nat,
sum-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,
MMTree-ext,
int_formula_prop_eq_lemma,
intformeq_wf,
lelt_wf,
false_wf,
int_seg_subtype,
decidable__equal_int,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
int_seg_properties,
int_seg_wf,
MMTree_size_wf,
le_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
isect_memberFormation,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
because_Cache,
productElimination,
unionElimination,
setEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
promote_hyp,
tokenEquality,
equalityElimination,
instantiate,
cumulativity,
atomEquality,
imageElimination,
equalityEquality,
addEquality,
universeEquality,
imageMemberEquality,
baseClosed,
pointwiseFunctionality,
baseApply,
closedConclusion,
addLevel,
levelHypothesis,
substitution
Latex:
\mforall{}T:Type. \mforall{}t:MMTree(T). (MMTree-rank(t) \mmember{} \mBbbN{})
Date html generated:
2016_05_16-AM-08_55_48
Last ObjectModification:
2016_01_17-AM-09_43_23
Theory : C-semantics
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