Nuprl Lemma : consensus-rcvs-to-consensus-events_wf
∀[V:Type]. ∀[A:Id List]. ∀[t:ℕ+]. ∀[f:(V List) ⟶ V]. ∀[v0:V]. ∀[L:consensus-rcv(V;A) List].
(consensus-rcvs-to-consensus-events(f;t;v0;L) ∈ consensus-event(V;A) List × (consensus-rcv(V;A) List))
Proof
Definitions occuring in Statement :
consensus-rcvs-to-consensus-events: consensus-rcvs-to-consensus-events(f;t;v0;L),
consensus-rcv: consensus-rcv(V;A),
consensus-event: consensus-event(V;A),
Id: Id,
list: T List,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
consensus-rcvs-to-consensus-events: consensus-rcvs-to-consensus-events(f;t;v0;L),
so_lambda: λ2x y.t[x; y],
prop: ℙ,
nat_plus: ℕ+,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
spreadn: spread3,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b]
Latex:
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[f:(V List) {}\mrightarrow{} V]. \mforall{}[v0:V]. \mforall{}[L:consensus-rcv(V;A) List].
(consensus-rcvs-to-consensus-events(f;t;v0;L) \mmember{} consensus-event(V;A) List
\mtimes{} (consensus-rcv(V;A) List))
Date html generated:
2016_05_16-PM-00_48_49
Last ObjectModification:
2016_01_17-PM-07_57_35
Theory : event-ordering
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