Nuprl Lemma : RankEx2co-ext
∀[S,T:Type].
RankEx2co(S;T) ≡ lbl:Atom × if lbl =a "LeafT" then T
if lbl =a "LeafS" then S
if lbl =a "Prod" then RankEx2co(S;T) × S × T
if lbl =a "Union" then S × RankEx2co(S;T) + RankEx2co(S;T)
if lbl =a "ListProd" then (S × RankEx2co(S;T)) List
if lbl =a "UnionList" then T + (RankEx2co(S;T) List)
else Void
fi
Proof
Definitions occuring in Statement :
RankEx2co: RankEx2co(S;T),
list: T List,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
union: left + right,
token: "$token",
atom: Atom,
void: Void,
universe: Type
Lemmas :
corec-ext,
eq_atom_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
eqtt_to_assert,
assert_of_eq_atom,
list_wf,
subtype_rel_product,
subtype_rel_sum,
subtype_rel_list,
subtype_rel_wf,
strong-continuous-depproduct,
continuous-constant,
strong-continuous-product,
continuous-id,
strong-continuous-union,
strong-continuous-list,
subtype_rel_weakening,
nat_wf
\mforall{}[S,T:Type].
RankEx2co(S;T) \mequiv{} lbl:Atom \mtimes{} if lbl =a "LeafT" then T
if lbl =a "LeafS" then S
if lbl =a "Prod" then RankEx2co(S;T) \mtimes{} S \mtimes{} T
if lbl =a "Union" then S \mtimes{} RankEx2co(S;T) + RankEx2co(S;T)
if lbl =a "ListProd" then (S \mtimes{} RankEx2co(S;T)) List
if lbl =a "UnionList" then T + (RankEx2co(S;T) List)
else Void
fi
Date html generated:
2015_07_17-AM-07_48_51
Last ObjectModification:
2015_01_27-AM-09_40_00
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