Nuprl Lemma : es-closed-open-interval-decomp-mem
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e1,e2,e:E].
([e1;e2) = ([e1;e) @ [e;e2)) ∈ (E List)) supposing (e1 ≤loc e and e ≤loc e2 )
Proof
Definitions occuring in Statement :
event-ordering+: EO+(Info),
es-closed-open-interval: [e;e'),
es-le: e ≤loc e' ,
es-E: E,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-le: e ≤loc e' ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e1,e2,e:E].
([e1;e2) = ([e1;e) @ [e;e2))) supposing (e1 \mleq{}loc e and e \mleq{}loc e2 )
Date html generated:
2016_05_16-PM-01_13_03
Last ObjectModification:
2016_01_17-PM-07_56_04
Theory : event-ordering
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