Step
*
1
1
of Lemma
iseg-es-hist
1. [Info] : Type
2. es : EO+(Info)@i'
3. e1 : E@i
4. WellFnd{i}(E;x,y.(x <loc y))
5. j : E@i
6. ∀k:E
((k <loc j)
⇒ (∀L:Info List
(L ≤ es-hist(es;e1;k)
⇒ ∃e∈[e1,k].L = es-hist(es;e1;e) ∈ (Info List)) supposing
((¬(L = [] ∈ (Info List))) and
(loc(e1) = loc(k) ∈ Id))))@i
7. L : Info List@i
8. loc(e1) = loc(j) ∈ Id
9. ¬(L = [] ∈ (Info List))
10. L ≤ map(λe.info(e);[])@i
11. ¬e1 ≤loc j
⊢ e1 ≤loc j
BY
{ ((D (-3)) THEN (Reduce (-2))) }
1
1. Info : Type
2. es : EO+(Info)@i'
3. e1 : E@i
4. WellFnd{i}(E;x,y.(x <loc y))
5. j : E@i
6. ∀k:E
((k <loc j)
⇒ (∀L:Info List
(L ≤ es-hist(es;e1;k)
⇒ ∃e∈[e1,k].L = es-hist(es;e1;e) ∈ (Info List)) supposing
((¬(L = [] ∈ (Info List))) and
(loc(e1) = loc(k) ∈ Id))))@i
7. L : Info List@i
8. loc(e1) = loc(j) ∈ Id
9. L ≤ []@i
10. ¬e1 ≤loc j
⊢ L = [] ∈ (Info List)
Latex:
1. [Info] : Type
2. es : EO+(Info)@i'
3. e1 : E@i
4. WellFnd\{i\}(E;x,y.(x <loc y))
5. j : E@i
6. \mforall{}k:E
((k <loc j)
{}\mRightarrow{} (\mforall{}L:Info List
(L \mleq{} es-hist(es;e1;k) {}\mRightarrow{} \mexists{}e\mmember{}[e1,k].L = es-hist(es;e1;e)) supposing
((\mneg{}(L = [])) and
(loc(e1) = loc(k)))))@i
7. L : Info List@i
8. loc(e1) = loc(j)
9. \mneg{}(L = [])
10. L \mleq{} map(\mlambda{}e.info(e);[])@i
11. \mneg{}e1 \mleq{}loc j
\mvdash{} e1 \mleq{}loc j
By
((D (-3)) THEN (Reduce (-2)))
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