Step
*
1
1
of Lemma
iseg-global-order-history
.....subterm..... T:t
2:n
1. Info : Type
2. L1 : (Id × Info) List@i
3. L2 : (Id × Info) List@i
4. L1 ≤ L2@i
5. e : E@i
6. ||L1|| ≤ ||L2||
7. loc(e) = loc(e) ∈ Id
8. f : (Id × Info) ─→ Info@i
9. (λx.(snd(x))) = f ∈ ((Id × Info) ─→ Info)@i
10. test : (Id × Info) ─→ 𝔹@i
11. (λx.fst(x) = loc(e)) = test ∈ ((Id × Info) ─→ 𝔹)@i
⊢ filter(test;firstn(e + 1;L2)) = filter(test;firstn(e + 1;L1)) ∈ Id × Info List+
BY
{ (All (RWO "global-eo-E-sq") THENA Auto) }
1
1. Info : Type
2. L1 : (Id × Info) List@i
3. L2 : (Id × Info) List@i
4. L1 ≤ L2@i
5. e : {e:ℕ||L1||| True} @i
6. ||L1|| ≤ ||L2||
7. loc(e) = loc(e) ∈ Id
8. f : (Id × Info) ─→ Info@i
9. (λx.(snd(x))) = f ∈ ((Id × Info) ─→ Info)@i
10. test : (Id × Info) ─→ 𝔹@i
11. (λx.fst(x) = loc(e)) = test ∈ ((Id × Info) ─→ 𝔹)@i
⊢ filter(test;firstn(e + 1;L2)) = filter(test;firstn(e + 1;L1)) ∈ Id × Info List+
Latex:
Latex:
.....subterm..... T:t
2:n
1. Info : Type
2. L1 : (Id \mtimes{} Info) List@i
3. L2 : (Id \mtimes{} Info) List@i
4. L1 \mleq{} L2@i
5. e : E@i
6. ||L1|| \mleq{} ||L2||
7. loc(e) = loc(e)
8. f : (Id \mtimes{} Info) {}\mrightarrow{} Info@i
9. (\mlambda{}x.(snd(x))) = f@i
10. test : (Id \mtimes{} Info) {}\mrightarrow{} \mBbbB{}@i
11. (\mlambda{}x.fst(x) = loc(e)) = test@i
\mvdash{} filter(test;firstn(e + 1;L2)) = filter(test;firstn(e + 1;L1))
By
Latex:
(All (RWO "global-eo-E-sq") THENA Auto)
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