Nuprl Lemma : std-initial-property
∀[M:Type ⟶ Type]. ∀[S:System(P.M[P])]. ∀[r:pRunType(P.M[P])]. run-initialization(r;snd(S)) supposing std-initial(S)
Proof
Definitions occuring in Statement :
std-initial: std-initial(S),
run-initialization: run-initialization(r;G),
pRunType: pRunType(T.M[T]),
System: System(P.M[P]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi2: snd(t),
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
System: System(P.M[P]),
run-initialization: run-initialization(r;G),
lg-all: ∀x∈G.P[x],
all: ∀x:A. B[x],
pi2: snd(t),
std-initial: std-initial(S),
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
ldag: LabeledDAG(T),
subtype_rel: A ⊆r B,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
pInTransit: pInTransit(P.M[P]),
pi1: fst(t)
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[S:System(P.M[P])].
\mforall{}[r:pRunType(P.M[P])]. run-initialization(r;snd(S)) supposing std-initial(S)
Date html generated:
2016_05_17-AM-10_51_39
Last ObjectModification:
2016_01_18-AM-00_12_51
Theory : process-model
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