Nuprl Lemma : es-interval-induction2
∀es:EO. ∀i:Id.
∀[P:e1:{e:E| loc(e) = i ∈ Id} ─→ {e2:E| loc(e2) = i ∈ Id} ─→ ℙ]
(∀e1@i.∀e2≥e1.(∀e:E. ((e1 <loc e) ⇒ e ≤loc e2 ⇒ P[e;e2])) ⇒ P[e1;e2]
⇒ ∀e1@i.∀e2<e1.P[e1;e2]
⇒ (∀e,e':E. (P[e;e']) supposing ((loc(e') = i ∈ Id) and (loc(e) = i ∈ Id))))
Proof
Definitions occuring in Statement :
alle-lt: ∀e<e'.P[e],
alle-ge: ∀e'≥e.P[e'],
alle-at: ∀e@i.P[e],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uimplies: b supposing a,
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
Lemmas :
es-interval-induction,
decidable__es-le,
decidable__es-locl,
es-le-not-locl,
equal_wf,
Id_wf,
es-loc_wf,
es-E_wf,
all_wf,
es-locl_wf,
es-le_wf,
es-le-loc,
event_ordering_wf
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:e1:\{e:E| loc(e) = i\} {}\mrightarrow{} \{e2:E| loc(e2) = i\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e1@i.\mforall{}e2\mgeq{}e1.(\mforall{}e:E. ((e1 <loc e) {}\mRightarrow{} e \mleq{}loc e2 {}\mRightarrow{} P[e;e2])) {}\mRightarrow{} P[e1;e2]
{}\mRightarrow{} \mforall{}e1@i.\mforall{}e2<e1.P[e1;e2]
{}\mRightarrow{} (\mforall{}e,e':E. (P[e;e']) supposing ((loc(e') = i) and (loc(e) = i))))
Date html generated:
2015_07_17-AM-08_51_24
Last ObjectModification:
2015_01_27-PM-01_18_19
Home
Index