Nuprl Lemma : C_TYPE-rank_wf
∀[ctyp:C_TYPE()]. (C_TYPE-rank(ctyp) ∈ ℕ)
Proof
Definitions occuring in Statement :
C_TYPE-rank: C_TYPE-rank(ctyp),
C_TYPE: C_TYPE(),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
C_TYPE-rank: C_TYPE-rank(ctyp),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
so_apply: x[s],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
so_apply: x[s1;s2;s3],
subtype_rel: A ⊆r B,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
length_wf,
int_seg_wf,
iff_weakening_equal,
top_wf,
subtype_rel_product,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_seg_properties,
select_wf,
spread_to_pi12,
subtype_rel-equal,
zero-le-nat,
length_wf_nat,
non_neg_sum,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
list_wf,
l_member_wf,
C_TYPE_wf,
l_all_wf2,
le_wf,
false_wf,
nat_wf,
C_TYPE_ind_wf_simple
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
because_Cache,
lambdaEquality,
productEquality,
atomEquality,
setElimination,
rename,
productElimination,
setEquality,
independent_pairEquality,
addEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
spreadEquality,
equalityEquality,
independent_functionElimination,
instantiate,
imageElimination
Latex:
\mforall{}[ctyp:C\_TYPE()]. (C\_TYPE-rank(ctyp) \mmember{} \mBbbN{})
Date html generated:
2016_05_16-AM-08_46_21
Last ObjectModification:
2016_01_17-AM-09_44_04
Theory : C-semantics
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