Nuprl Lemma : chosen-command_wf
∀[M:Type ⟶ Type]. ∀[r:fulpRunType(P.M[P])]. ∀[t:ℕ+]. ∀[x:pInTransit(P.M[P])]. ∀[env:pEnvType(P.M[P])].
(chosen-command(P.M[P];env;r;t;x) ∈ ℙ)
Proof
Definitions occuring in Statement :
chosen-command: chosen-command(P.M[P];env;r;t;x),
pEnvType: pEnvType(T.M[T]),
fulpRunType: fulpRunType(T.M[T]),
pInTransit: pInTransit(P.M[P]),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
chosen-command: chosen-command(P.M[P];env;r;t;x),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
ldag: LabeledDAG(T),
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
pEnvType: pEnvType(T.M[T]),
fulpRunType: fulpRunType(T.M[T]),
nat_plus: ℕ+,
uimplies: b supposing a,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
System: System(P.M[P]),
top: Top,
lg-is-source: lg-is-source(g;i),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[r:fulpRunType(P.M[P])]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[x:pInTransit(P.M[P])].
\mforall{}[env:pEnvType(P.M[P])].
(chosen-command(P.M[P];env;r;t;x) \mmember{} \mBbbP{})
Date html generated:
2016_05_17-AM-10_54_35
Last ObjectModification:
2015_12_29-PM-05_19_02
Theory : process-model
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