Step
*
2
1
2
1
of Lemma
global-order-compat-combine
1. [Info] : Type
2. L1 : (Id × Info) List@i
3. ys : (Id × Info) List@i
4. y : Id × Info@i
5. ∀i:Id. filter(λx.fst(x) = i;L1) || filter(λx.fst(x) = i;ys @ [y])@i
6. i : Id@i
7. filter(λx.fst(x) = i;ys @ [y]) ≤ filter(λx.fst(x) = i;L1)
⊢ filter(λx.fst(x) = i;ys) ≤ filter(λx.fst(x) = i;L1)
BY
{ (Using [`l2',⌈filter(λx.fst(x) = i;ys @ [y])⌉] (BLemma `iseg_transitivity`)⋅ THEN Auto) }
Latex:
Latex:
1. [Info] : Type
2. L1 : (Id \mtimes{} Info) List@i
3. ys : (Id \mtimes{} Info) List@i
4. y : Id \mtimes{} Info@i
5. \mforall{}i:Id. filter(\mlambda{}x.fst(x) = i;L1) || filter(\mlambda{}x.fst(x) = i;ys @ [y])@i
6. i : Id@i
7. filter(\mlambda{}x.fst(x) = i;ys @ [y]) \mleq{} filter(\mlambda{}x.fst(x) = i;L1)
\mvdash{} filter(\mlambda{}x.fst(x) = i;ys) \mleq{} filter(\mlambda{}x.fst(x) = i;L1)
By
Latex:
(Using [`l2',\mkleeneopen{}filter(\mlambda{}x.fst(x) = i;ys @ [y])\mkleeneclose{}] (BLemma `iseg\_transitivity`)\mcdot{} THEN Auto)
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