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
Home
Index