Nuprl Lemma : pRun_functionality
∀[M:Type ⟶ Type]
∀[nat2msg:ℕ ⟶ pMsg(P.M[P])]. ∀[loc2msg:Id ⟶ pMsg(P.M[P])]. ∀[env:pEnvType(P.M[P])]. ∀[S1,S2:System(P.M[P])].
pRun(S1;env;nat2msg;loc2msg) = pRun(S2;env;nat2msg;loc2msg) ∈ pRunType(P.M[P]) supposing system-equiv(P.M[P];S1;S2)
supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
pRun: pRun(S0;env;nat2msg;loc2msg),
pEnvType: pEnvType(T.M[T]),
pRunType: pRunType(T.M[T]),
system-equiv: system-equiv(T.M[T];S1;S2),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
strong-type-continuous: Continuous+(T.F[T]),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
pRunType: pRunType(T.M[T]),
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
pRun: pRun(S0;env;nat2msg;loc2msg),
ycomb: Y,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
pi2: snd(t),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
ge: i ≥ j ,
int_upper: {i...},
fulpRunType: fulpRunType(T.M[T]),
System: System(P.M[P]),
cand: A c∧ B,
pEnvType: pEnvType(T.M[T]),
nat_plus: ℕ+,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True,
spreadn: spread3,
system-equiv: system-equiv(T.M[T];S1;S2),
do-chosen-command: do-chosen-command(nat2msg;loc2msg;t;S;n;m;nm),
ldag: LabeledDAG(T),
squash: ↓T,
let: let,
lg-is-source: lg-is-source(g;i),
pInTransit: pInTransit(P.M[P]),
pi1: fst(t),
Id: Id,
create-component: create-component(t;P;x;Cs;L),
select: L[n],
cons: [a / b],
process-equiv: process-equiv,
component: component(P.M[P]),
nequal: a ≠ b ∈ T
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}[nat2msg:\mBbbN{} {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[loc2msg:Id {}\mrightarrow{} pMsg(P.M[P])]. \mforall{}[env:pEnvType(P.M[P])].
\mforall{}[S1,S2:System(P.M[P])].
pRun(S1;env;nat2msg;loc2msg) = pRun(S2;env;nat2msg;loc2msg)
supposing system-equiv(P.M[P];S1;S2)
supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_40_56
Last ObjectModification:
2016_01_18-AM-00_23_04
Theory : process-model
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