Nuprl Lemma : data-stream-append
∀[as1,as2:Top List]. ∀[P:Top]. (data-stream(P;as1 @ as2) ~ data-stream(P;as1) @ data-stream(P*(as1);as2))
Proof
Definitions occuring in Statement :
data-stream: data-stream(P;L),
iterate-dataflow: P*(inputs),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b)
Latex:
\mforall{}[as1,as2:Top List]. \mforall{}[P:Top].
(data-stream(P;as1 @ as2) \msim{} data-stream(P;as1) @ data-stream(P*(as1);as2))
Date html generated:
2016_05_17-AM-10_21_19
Last ObjectModification:
2016_01_18-AM-00_20_31
Theory : process-model
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