Nuprl Lemma : disjoint-union-comb-classrel
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
∀v:A + B. uiff(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),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
union: left + right,
universe: Type
Lemmas :
parallel-classrel,
simple-comb-1_wf,
lifting-1_wf,
simple-comb-1-classrel,
and_wf,
equal_wf,
isl_wf,
btrue_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
outl_wf,
assert_wf,
classrel_wf,
not_wf,
not_assert_elim,
btrue_neq_bfalse,
assert_elim,
bfalse_wf,
outr_wf,
squash_wf,
bnot_wf,
assert_of_bnot,
sq_stable__classrel,
true_wf,
false_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. uiff(v \mmember{} X (+) Y(e);((\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_17
Last ObjectModification:
2015_01_28-AM-10_45_57
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