Nuprl Lemma : sequence-classrel
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[Z:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:A].
uiff(v ∈ sequence-class(X;Y;Z)(e);↓((∀e':E. (e' ≤loc e ⇒ (↑e' ∈b Y) ⇒ (↑e' ∈b X))) ∧ v ∈ X(e))
∨ (∃e':E
(e' ≤loc e
∧ (↑e' ∈b Y)
∧ (¬↑e' ∈b X)
∧ (∀e'':E. ((e'' <loc e') ⇒ (↑e'' ∈b Y) ⇒ (↑e'' ∈b X)))
∧ v ∈ Z(e))))
Proof
Definitions occuring in Statement :
sequence-class: sequence-class(X;Y;Z),
classrel: v ∈ X(e),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
sequence-class: sequence-class(X;Y;Z),
exists: ∃x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
bfalse: ff,
false: False,
sq_exists: ∃x:{A| B[x]},
cand: A c∧ B,
class-ap: X(e),
not: ¬A,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
true: True,
sq_stable: SqStable(P)
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:A].
uiff(v \mmember{} sequence-class(X;Y;Z)(e);\mdownarrow{}((\mforall{}e':E. (e' \mleq{}loc e {}\mRightarrow{} (\muparrow{}e' \mmember{}\msubb{} Y) {}\mRightarrow{} (\muparrow{}e' \mmember{}\msubb{} X))) \mwedge{} v \mmember{} X(e))
\mvee{} (\mexists{}e':E
(e' \mleq{}loc e
\mwedge{} (\muparrow{}e' \mmember{}\msubb{} Y)
\mwedge{} (\mneg{}\muparrow{}e' \mmember{}\msubb{} X)
\mwedge{} (\mforall{}e'':E. ((e'' <loc e') {}\mRightarrow{} (\muparrow{}e'' \mmember{}\msubb{} Y) {}\mRightarrow{} (\muparrow{}e'' \mmember{}\msubb{} X)))
\mwedge{} v \mmember{} Z(e))))
Date html generated:
2016_05_17-AM-00_24_44
Last ObjectModification:
2016_01_17-PM-06_50_13
Theory : event-ordering
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