### Nuprl Lemma : es-interval-induction

`∀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])`

Proof

Definitions occuring in Statement :  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` 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 :  alle-at_wf all_wf es-le_wf es-locl_wf es-le-loc es-E_wf Id_wf es-loc_wf event_ordering_wf le_wf length_wf es-interval_wf subtract_wf set_wf less_than_wf primrec-wf2 nat_wf equal_wf es-le-self member-es-interval non_neg_length length_wf_nat length_zero member-implies-null-eq-bfalse and_wf list_wf null_wf3 subtype_rel_list top_wf null_nil_lemma btrue_wf btrue_neq_bfalse es-interval-partition length-append es-le-pred es-locl-first assert_elim assert_wf es-first_wf2 es-interval-non-zero es-pred_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\mgeq{}e1.P[e1;e2])

Date html generated: 2015_07_17-AM-08_51_20
Last ObjectModification: 2015_01_27-PM-01_20_16

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