Nuprl Lemma : es-before-decomp
∀the_es:EO. ∀e',e:E. ((e ∈ before(e')) ⇒ (∃l:E List. (before(e') = (before(e) @ [e] @ l) ∈ (E List))))
Proof
Definitions occuring in Statement :
es-before: before(e),
es-E: E,
event_ordering: EO,
l_member: (x ∈ l),
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
squash: ↓T,
true: True,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
guard: {T},
rev_implies: P ⇐ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Latex:
\mforall{}the$_{es}$:EO. \mforall{}e',e:E. ((e \mmember{} before(e')) {}\mRightarrow{} (\mexists{}l:E List. (before(e') = (before\000C(e) @ [e] @ l))))
Date html generated:
2016_05_16-AM-09_37_02
Last ObjectModification:
2016_01_17-PM-01_32_29
Theory : new!event-ordering
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