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
Definitions unfolded in proof :
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
pi_term: pi_term(),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
pi_termco_size: pi_termco_size(p),
has-value: (a)↓,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
pi_term_size: pi_term_size(p),
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A
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:
2016_05_17-AM-11_20_51
Last ObjectModification:
2016_01_18-AM-07_49_24
Theory : event-logic-applications
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