Nuprl Lemma : classfun-res-disjoint-union-comb-as-parallel-eclass1
∀[Info,A,B,S:Type]. ∀[es:EO+(Info)]. ∀[X1:EClass(A)]. ∀[X2:EClass(B)]. ∀[e:E]. ∀[f1:Id ⟶ A ⟶ S ⟶ S]. ∀[f2:Id
⟶ B
⟶ S
⟶ S].
∀[s:S].
((f1 + f2 loc(e) X1 (+) X2@e s) = ((f1 o X1) || (f2 o X2)@e s) ∈ S) supposing
(disjoint-classrel(es;A;X1;B;X2) and
single-valued-classrel(es;X1;A) and
single-valued-classrel(es;X2;B) and
((↑e ∈b X1) ∨ (↑e ∈b X2)))
Proof
Definitions occuring in Statement :
disjoint-union-tr: tr1 + tr2,
disjoint-union-comb: X (+) Y,
parallel-class: X || Y,
eclass1: (f o X),
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
or: P ∨ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
prop: ℙ,
implies: P ⇒ Q,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
all: ∀x:A. B[x],
top: Top
Latex:
\mforall{}[Info,A,B,S:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X1:EClass(A)]. \mforall{}[X2:EClass(B)]. \mforall{}[e:E]. \mforall{}[f1:Id
{}\mrightarrow{} A
{}\mrightarrow{} S
{}\mrightarrow{} S].
\mforall{}[f2:Id {}\mrightarrow{} B {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[s:S].
((f1 + f2 loc(e) X1 (+) X2@e s) = ((f1 o X1) || (f2 o X2)@e s)) supposing
(disjoint-classrel(es;A;X1;B;X2) and
single-valued-classrel(es;X1;A) and
single-valued-classrel(es;X2;B) and
((\muparrow{}e \mmember{}\msubb{} X1) \mvee{} (\muparrow{}e \mmember{}\msubb{} X2)))
Date html generated:
2016_05_17-AM-11_16_43
Last ObjectModification:
2015_12_29-PM-05_12_04
Theory : process-model
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