Nuprl Lemma : classfun-res-parallel-class-left
∀[Info,A:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(A)]. ∀[e:E].
(X || Y@e ~ X@e) supposing (disjoint-classrel(es;A;X;A;Y) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
classfun-res: X@e,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
classfun-res: X@e,
parallel-class: X || Y,
classfun: X(e),
eclass-compose2: eclass-compose2(f;X;Y),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
all: ∀x:A. B[x],
member: t ∈ T,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
squash: ↓T,
false: False,
exists: ∃x:A. B[x],
not: ¬A,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Latex:
\mforall{}[Info,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(A)]. \mforall{}[e:E].
(X || Y@e \msim{} X@e) supposing (disjoint-classrel(es;A;X;A;Y) and (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_17-AM-11_15_58
Last ObjectModification:
2015_12_29-PM-05_12_23
Theory : process-model
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