Nuprl Lemma : es-interface-predecessors-last
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E(X)]. ((¬↑null(≤(X)(e))) ∧ (last(≤(X)(e)) = e ∈ E(X)))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
last: last(L),
null: null(as),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
es-E-interface: E(X),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
squash: ↓T,
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
band: p ∧b q
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E(X)].
((\mneg{}\muparrow{}null(\mleq{}(X)(e))) \mwedge{} (last(\mleq{}(X)(e)) = e))
Date html generated:
2016_05_17-AM-06_56_28
Last ObjectModification:
2016_01_17-PM-06_37_52
Theory : event-ordering
Home
Index