Nuprl Lemma : pi_term-ext
pi_term() ≡ lbl:Atom × if lbl =a "zero" then Unit
if lbl =a "comm" then pre:pi_prefix() × pi_term()
if lbl =a "option" then left:pi_term() × pi_term()
if lbl =a "par" then left:pi_term() × pi_term()
if lbl =a "rep" then pi_term()
if lbl =a "new" then name:Name × pi_term()
else Void
fi
Proof
Definitions occuring in Statement :
pi_term: pi_term(),
pi_prefix: pi_prefix(),
name: Name,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
ext-eq: A ≡ B,
unit: Unit,
product: x:A × B[x],
token: "$token",
atom: Atom,
void: Void
Lemmas :
pi_termco-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_wf2,
unit_subtype_base,
it_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
value-type-has-value,
int-value-type,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
pi_termco_size_wf,
pi_term_wf,
pi_prefix_wf,
name_wf,
pi_termco_wf,
add-nat,
false_wf,
pi_term_size_wf,
nat_properties
Latex:
pi\_term() \mequiv{} lbl:Atom \mtimes{} if lbl =a "zero" then Unit
if lbl =a "comm" then pre:pi\_prefix() \mtimes{} pi\_term()
if lbl =a "option" then left:pi\_term() \mtimes{} pi\_term()
if lbl =a "par" then left:pi\_term() \mtimes{} pi\_term()
if lbl =a "rep" then pi\_term()
if lbl =a "new" then name:Name \mtimes{} pi\_term()
else Void
fi
Date html generated:
2015_07_23-AM-11_31_59
Last ObjectModification:
2015_05_04-PM-06_19_00
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