Nuprl Lemma : es-pplus-first-since-exit
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[Q,R:{e:E| loc(e) = loc(e1) ∈ Id} ⟶ ℙ].
((∀e:{e:E| loc(e) = loc(e1) ∈ Id} . Dec(Q[e]))
⇒ ([e1,e2]~([a,b].b = first e ≥ a.Q[e] ∧ ∀e∈[a,b).¬R[e])+ ⇐⇒ e1 ≤loc e2 ∧ Q[e2] ∧ ∀e∈[e1,e2].R[e] ⇒ Q[e]))
Proof
Definitions occuring in Statement :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
es-first-since: e2 = first e ≥ e1.P[e],
alle-between2: ∀e∈[e1,e2].P[e],
alle-between1: ∀e∈[e1,e2).P[e],
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
and: 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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
so_apply: x[s1;s2],
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
guard: {T},
cand: A c∧ B,
alle-between1: ∀e∈[e1,e2).P[e],
alle-between2: ∀e∈[e1,e2].P[e],
es-le: e ≤loc e' ,
or: P ∨ Q,
not: ¬A,
false: False,
es-first-since: e2 = first e ≥ e1.P[e],
squash: ↓T
Latex:
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[Q,R:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
((\mforall{}e:\{e:E| loc(e) = loc(e1)\} . Dec(Q[e]))
{}\mRightarrow{} ([e1,e2]\msim{}([a,b].b = first e \mgeq{} a.Q[e] \mwedge{} \mforall{}e\mmember{}[a,b).\mneg{}R[e])+
\mLeftarrow{}{}\mRightarrow{} e1 \mleq{}loc e2 \mwedge{} Q[e2] \mwedge{} \mforall{}e\mmember{}[e1,e2].R[e] {}\mRightarrow{} Q[e]))
Date html generated:
2016_05_16-AM-09_59_08
Last ObjectModification:
2016_01_17-PM-01_23_27
Theory : new!event-ordering
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