Nuprl Lemma : choosable-command_wf
∀[M:Type ⟶ Type]. ∀[r:pRunType(P.M[P])]. ∀[t:ℕ+]. ∀[x:pInTransit(P.M[P])]. (choosable-command(P.M[P];r;t;x) ∈ ℙ)
Proof
Definitions occuring in Statement :
choosable-command: choosable-command(P.M[P];r;t;x),
pRunType: pRunType(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 :
choosable-command: choosable-command(P.M[P];r;t;x),
run-system: run-system(r;t),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
ldag: LabeledDAG(T),
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
subtype_rel: A ⊆r B,
lg-is-source: lg-is-source(g;i),
uimplies: b supposing a,
not: ¬A,
false: False,
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:pRunType(P.M[P])]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[x:pInTransit(P.M[P])].
(choosable-command(P.M[P];r;t;x) \mmember{} \mBbbP{})
Date html generated:
2016_05_17-AM-10_53_58
Last ObjectModification:
2015_12_29-PM-05_19_08
Theory : process-model
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