Nuprl Lemma : rank-Ex1_wf
∀[T:Type]. ∀[t:RankEx1(T)]. (rank-Ex1(t) ∈ ℕ)
Proof
Definitions occuring in Statement :
rank-Ex1: rank-Ex1(t),
RankEx1: RankEx1(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
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 ,
RankEx1_Leaf: RankEx1_Leaf(leaf),
RankEx1_size: RankEx1_size(p),
rank-Ex1: rank-Ex1(t),
RankEx1_Leaf?: RankEx1_Leaf?(v),
pi1: fst(t),
RankEx1_Prod?: RankEx1_Prod?(v),
RankEx1_Prod-prod: RankEx1_Prod-prod(v),
RankEx1_ProdL?: RankEx1_ProdL?(v),
RankEx1_ProdL-prodl: RankEx1_ProdL-prodl(v),
RankEx1_ProdR?: RankEx1_ProdR?(v),
RankEx1_ProdR-prodr: RankEx1_ProdR-prodr(v),
RankEx1_List-list: RankEx1_List-list(v),
pi2: snd(t),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
RankEx1_Prod: RankEx1_Prod(prod),
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
RankEx1_ProdL: RankEx1_ProdL(prodl),
RankEx1_ProdR: RankEx1_ProdR(prodr),
RankEx1_List: RankEx1_List(list),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
upto_wf,
map_wf,
top_wf,
subtype_rel_list,
map-as-map-upto,
imax-list-is-nat,
add-nat,
sum-nat-less,
length_wf,
select_wf,
RankEx1_wf,
length_wf_nat,
sum-nat,
add-is-int-iff,
imax_nat,
add_nat_wf,
nat_wf,
imax_wf,
int_term_value_add_lemma,
itermAdd_wf,
decidable__lt,
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,
RankEx1-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,
RankEx1_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,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
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,
addEquality,
pointwiseFunctionality,
baseApply,
closedConclusion,
baseClosed,
equalityEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:RankEx1(T)]. (rank-Ex1(t) \mmember{} \mBbbN{})
Date html generated:
2016_05_16-AM-08_58_58
Last ObjectModification:
2016_01_17-AM-09_42_27
Theory : C-semantics
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