Nuprl Lemma : disjoint-union-comb-classrel-weak
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
∀v:A + B. (v ∈ X (+) Y(e) ⇐⇒ ((↑isl(v)) ∧ outl(v) ∈ X(e)) ∨ ((¬↑isl(v)) ∧ outr(v) ∈ Y(e)))
Proof
Definitions occuring in Statement :
disjoint-union-comb: X (+) Y,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
outr: outr(x),
outl: outl(x),
assert: ↑b,
isl: isl(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
union: left + right,
universe: Type
Lemmas :
disjoint-union-comb-classrel,
classrel_wf,
disjoint-union-comb_wf,
or_wf,
assert_wf,
isl_wf,
not_wf,
not_assert_elim,
btrue_wf,
btrue_neq_bfalse,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}v:A + B. (v \mmember{} X (+) Y(e) \mLeftarrow{}{}\mRightarrow{} ((\muparrow{}isl(v)) \mwedge{} outl(v) \mmember{} X(e)) \mvee{} ((\mneg{}\muparrow{}isl(v)) \mwedge{} outr(v) \mmember{} Y(e)))
Date html generated:
2015_07_22-PM-00_19_19
Last ObjectModification:
2015_01_28-AM-10_42_20
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