Nuprl Lemma : Comm-process-q_aux_wf
∀[q:(Id × (pi_prefix() List)) List]
(Comm-process-q_aux(q) ∈ Id
⟶ st:Id fp-> pi_prefix() List
⟶ ((Id × (pi_prefix() List)) List × st:Id fp-> pi_prefix() List × Id × ((ℕ × Id × ℕ × Name) List)))
Proof
Definitions occuring in Statement :
Comm-process-q_aux: Comm-process-q_aux(q),
pi_prefix: pi_prefix(),
fpf: a:A fp-> B[a],
Id: Id,
name: Name,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
Comm-process-q_aux: Comm-process-q_aux(q),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
pi2: snd(t),
pi1: fst(t)
Latex:
\mforall{}[q:(Id \mtimes{} (pi\_prefix() List)) List]
(Comm-process-q\_aux(q) \mmember{} Id
{}\mrightarrow{} st:Id fp-> pi\_prefix() List
{}\mrightarrow{} ((Id \mtimes{} (pi\_prefix() List)) List
\mtimes{} st:Id fp-> pi\_prefix() List
\mtimes{} Id
\mtimes{} ((\mBbbN{} \mtimes{} Id \mtimes{} \mBbbN{} \mtimes{} Name) List)))
Date html generated:
2016_05_17-AM-11_33_32
Last ObjectModification:
2016_01_18-AM-07_46_58
Theory : event-logic-applications
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