Step
*
1
of Lemma
pv11_p1_pmax_wf
1. Cmd : ValueAllType
2. ldrs_uid : Id ─→ ℤ
⊢ λpvals.let g = λbn,slt,z. let bn',z = z in let s',z = z in (slt =z s') ∧b (bn < bn') in
let P = λz.let bn,z = z
in let s,c = z
in ¬b(∃zw∈pvals.g bn s zw)_b in
mapfilter(λx.(snd(x));P;pvals) ∈ ((pv11_p1_Ballot_Num() × ℤ × Cmd) List) ─→ ((ℤ × Cmd) List)
BY
{ (MemCD THEN Try (CompleteAuto)) }
1
.....subterm..... T:t
1:n
1. Cmd : ValueAllType
2. ldrs_uid : Id ─→ ℤ
3. pvals : (pv11_p1_Ballot_Num() × ℤ × Cmd) List@i
⊢ let g = λbn,slt,z. let bn',z = z in let s',z = z in (slt =z s') ∧b (bn < bn') in
let P = λz.let bn,z = z
in let s,c = z
in ¬b(∃zw∈pvals.g bn s zw)_b in
mapfilter(λx.(snd(x));P;pvals) ∈ (ℤ × Cmd) List
Latex:
Latex:
1. Cmd : ValueAllType
2. ldrs$_{uid}$ : Id {}\mrightarrow{} \mBbbZ{}
\mvdash{} \mlambda{}pvals.let g = \mlambda{}bn,slt,z. let bn',z = z in let s',z = z in (slt =\msubz{} s') \mwedge{}\msubb{} (bn < bn') in
let P = \mlambda{}z.let bn,z = z
in let s,c = z
in \mneg{}\msubb{}(\mexists{}zw\mmember{}pvals.g bn s zw)\_b in
mapfilter(\mlambda{}x.(snd(x));P;pvals) \mmember{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)
{}\mrightarrow{} ((\mBbbZ{} \mtimes{} Cmd) List)
By
Latex:
(MemCD THEN Try (CompleteAuto))
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