Nuprl Lemma : istype-mrecind
∀[L:MutualRectypeSpec]. ∀[P:mobj(L) ⟶ TYPE].  istype(mrecind(L;x.P[x]))
Proof
Definitions occuring in Statement : 
mrecind: mrecind(L;x.P[x])
, 
mobj: mobj(L)
, 
mrec_spec: MutualRectypeSpec
, 
istype: istype(T)
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
mrecind: mrecind(L;x.P[x])
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
mkinds: mKinds
, 
prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl)
, 
implies: P 
⇒ Q
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
int_seg: {i..j-}
, 
uimplies: b supposing a
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
le: A ≤ B
, 
less_than: a < b
, 
squash: ↓T
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
not: ¬A
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
top: Top
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
less_than': less_than'(a;b)
, 
mrec: mrec(L;i)
, 
uiff: uiff(P;Q)
, 
outl: outl(x)
, 
isl: isl(x)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
true: True
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
prec: prec(lbl,p.a[lbl; p];i)
, 
so_apply: x[s]
, 
ext-eq: A ≡ B
, 
cand: A c∧ B
, 
outr: outr(x)
, 
bnot: ¬bb
, 
bfalse: ff
, 
list: T List
, 
l_all: (∀x∈L.P[x])
Lemmas referenced : 
mkinds_wf, 
istype-less_than, 
length_wf, 
mrec-spec_wf, 
tuple-type_wf, 
map_wf, 
prec_wf, 
list_wf, 
istype-universe, 
mobj_wf, 
mrec_spec_wf, 
int_seg_wf, 
select_wf, 
int_seg_properties, 
decidable__le, 
full-omega-unsat, 
intformand_wf, 
intformnot_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
istype-int, 
int_formula_prop_and_lemma, 
istype-void, 
int_formula_prop_not_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_wf, 
decidable__lt, 
intformless_wf, 
int_formula_prop_less_lemma, 
select-tuple_wf, 
int_seg_subtype_nat, 
istype-false, 
select-map, 
subtype_rel_list, 
top_wf, 
equal_wf, 
squash_wf, 
true_wf, 
inl-one-one, 
outl_wf, 
assert_wf, 
btrue_wf, 
bfalse_wf, 
mrec_wf, 
btrue_neq_bfalse, 
not-0-eq-1, 
inr-one-one, 
subtype_rel_self, 
iff_weakening_equal, 
mobj-ext, 
map-length, 
outr_wf, 
bnot_wf, 
istype-true, 
mk-prec_wf, 
prec-arg-types_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
sqequalRule, 
Error :functionIsType, 
Error :universeIsType, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
setElimination, 
rename, 
Error :setIsType, 
Error :inhabitedIsType, 
natural_numberEquality, 
instantiate, 
unionEquality, 
cumulativity, 
atomEquality, 
universeEquality, 
Error :lambdaFormation_alt, 
Error :lambdaEquality_alt, 
equalityTransitivity, 
equalitySymmetry, 
unionElimination, 
Error :equalityIstype, 
dependent_functionElimination, 
independent_functionElimination, 
Error :unionIsType, 
applyLambdaEquality, 
because_Cache, 
Error :TYPEIsType, 
closedConclusion, 
independent_isectElimination, 
productElimination, 
imageElimination, 
approximateComputation, 
Error :dependent_pairFormation_alt, 
int_eqEquality, 
Error :isect_memberEquality_alt, 
voidElimination, 
independent_pairFormation, 
applyEquality, 
Error :dependent_set_memberEquality_alt, 
Error :productIsType, 
promote_hyp, 
hyp_replacement, 
Error :inlEquality_alt, 
imageMemberEquality, 
baseClosed, 
Error :TYPEMemberIsType, 
Error :dependent_pairEquality_alt, 
Error :inrEquality_alt
Latex:
\mforall{}[L:MutualRectypeSpec].  \mforall{}[P:mobj(L)  {}\mrightarrow{}  TYPE].    istype(mrecind(L;x.P[x]))
Date html generated:
2019_06_20-PM-02_16_02
Last ObjectModification:
2019_03_12-PM-11_10_11
Theory : tuples
Home
Index