Nuprl Lemma : mrecind_wf
∀[L:MutualRectypeSpec]. ∀[P:mobj(L) ⟶ ℙ]. (mrecind(L;x.P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
mrecind: mrecind(L;x.P[x])
,
mobj: mobj(L)
,
mrec_spec: MutualRectypeSpec
,
uall: ∀[x:A]. B[x]
,
prop: ℙ
,
so_apply: x[s]
,
member: t ∈ T
,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
mrecind: mrecind(L;x.P[x])
,
prop: ℙ
,
all: ∀x:A. B[x]
,
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
,
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
,
so_lambda: λ2x.t[x]
Lemmas referenced :
mkinds_wf,
less_than_wf,
length_wf,
mrec-spec_wf,
tuple-type_wf,
map_wf,
prec_wf,
list_wf,
istype-universe,
istype-less_than,
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,
true_wf,
select-tuple_wf,
int_seg_subtype_nat,
istype-false,
select-map,
subtype_rel_list,
top_wf,
equal_wf,
squash_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,
l_all_wf,
l_member_wf,
mk-prec_wf,
prec-arg-types_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
setEquality,
atomEquality,
natural_numberEquality,
instantiate,
unionEquality,
cumulativity,
universeEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
Error :lambdaEquality_alt,
equalityTransitivity,
equalitySymmetry,
unionElimination,
Error :equalityIstype,
dependent_functionElimination,
independent_functionElimination,
Error :unionIsType,
axiomEquality,
Error :functionIsType,
Error :universeIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
closedConclusion,
because_Cache,
independent_isectElimination,
productElimination,
imageElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
voidElimination,
independent_pairFormation,
applyEquality,
Error :dependent_set_memberEquality_alt,
Error :productIsType,
applyLambdaEquality,
promote_hyp,
hyp_replacement,
imageMemberEquality,
baseClosed,
Error :dependent_pairEquality_alt,
Error :setIsType
Latex:
\mforall{}[L:MutualRectypeSpec]. \mforall{}[P:mobj(L) {}\mrightarrow{} \mBbbP{}]. (mrecind(L;x.P[x]) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_15_58
Last ObjectModification:
2019_03_12-PM-10_51_10
Theory : tuples
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