Nuprl Lemma : es-pstar-q-partition
∀es:EO. ∀e1,e2,b:E.
∀[Q,P:{e:E| loc(e) = loc(e1) ∈ Id} ⟶ {e:E| loc(e) = loc(e1) ∈ Id} ⟶ ℙ].
((e1 <loc b)
⇒ b ≤loc e2
⇒ [e1;pred(b)]~([a,b].P[a;b])*[a,b].P[a;b]
⇒ [b;e2]~([a,b].P[a;b])*[a,b].Q[a;b]
⇒ [e1;e2]~([a,b].P[a;b])*[a,b].Q[a;b])
Proof
Definitions occuring in Statement :
es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b],
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
cand: A c∧ B,
prop: ℙ,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
subtract: n - m,
so_apply: x[s],
so_apply: x[s1;s2],
es-locl: (e <loc e'),
so_lambda: λ2x y.t[x; y],
less_than: a < b,
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-causl: (e < e'),
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}es:EO. \mforall{}e1,e2,b:E.
\mforall{}[Q,P:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
((e1 <loc b)
{}\mRightarrow{} b \mleq{}loc e2
{}\mRightarrow{} [e1;pred(b)]\msim{}([a,b].P[a;b])*[a,b].P[a;b]
{}\mRightarrow{} [b;e2]\msim{}([a,b].P[a;b])*[a,b].Q[a;b]
{}\mRightarrow{} [e1;e2]\msim{}([a,b].P[a;b])*[a,b].Q[a;b])
Date html generated:
2016_05_16-AM-09_56_32
Last ObjectModification:
2016_01_17-PM-01_32_54
Theory : new!event-ordering
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