Nuprl Lemma : pi_prefix-induction
∀[P:pi_prefix() ⟶ ℙ]
((∀chan,var:Name. P[pisend(chan;var)]) ⇒ (∀chan,var:Name. P[pircv(chan;var)]) ⇒ {∀v:pi_prefix(). P[v]})
Proof
Definitions occuring in Statement :
pircv: pircv(chan;var),
pisend: pisend(chan;var),
pi_prefix: pi_prefix(),
name: Name,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
guard: {T},
all: ∀x:A. B[x],
ext-eq: A ≡ B,
and: P ∧ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
sq_type: SQType(T),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
pisend: pisend(chan;var),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
false: False,
pircv: pircv(chan;var)
Latex:
\mforall{}[P:pi\_prefix() {}\mrightarrow{} \mBbbP{}]
((\mforall{}chan,var:Name. P[pisend(chan;var)])
{}\mRightarrow{} (\mforall{}chan,var:Name. P[pircv(chan;var)])
{}\mRightarrow{} \{\mforall{}v:pi\_prefix(). P[v]\})
Date html generated:
2016_05_17-AM-11_20_16
Last ObjectModification:
2015_12_29-PM-06_58_31
Theory : event-logic-applications
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