Step
*
3
of Lemma
three-cs-no-repeated-votes
1. V : Type@i'
2. A : Id List@i
3. t : ℕ+@i
4. f : (V List) ─→ V@i
⊢ ∀s,y:ts-reachable(three-consensus-ts(V;A;t;f)).
((∀a:{a:Id| (a ∈ A)} . no_repeats(consensus-rcv(V;A);filter(λx.rcv-vote?(x);s a)))
⇒ (s ts-rel(three-consensus-ts(V;A;t;f)) y)
⇒ (∀a:{a:Id| (a ∈ A)} . no_repeats(consensus-rcv(V;A);filter(λx.rcv-vote?(x);y a))))
BY
{ Auto }
1
1. V : Type@i'
2. A : Id List@i
3. t : ℕ+@i
4. f : (V List) ─→ V@i
5. s : ts-reachable(three-consensus-ts(V;A;t;f))@i
6. y : ts-reachable(three-consensus-ts(V;A;t;f))@i
7. ∀a:{a:Id| (a ∈ A)} . no_repeats(consensus-rcv(V;A);filter(λx.rcv-vote?(x);s a))@i
8. s ts-rel(three-consensus-ts(V;A;t;f)) y@i
9. a : {a:Id| (a ∈ A)} @i
⊢ no_repeats(consensus-rcv(V;A);filter(λx.rcv-vote?(x);y a))
Latex:
1. V : Type@i'
2. A : Id List@i
3. t : \mBbbN{}\msupplus{}@i
4. f : (V List) {}\mrightarrow{} V@i
\mvdash{} \mforall{}s,y:ts-reachable(three-consensus-ts(V;A;t;f)).
((\mforall{}a:\{a:Id| (a \mmember{} A)\} . no\_repeats(consensus-rcv(V;A);filter(\mlambda{}x.rcv-vote?(x);s a)))
{}\mRightarrow{} (s ts-rel(three-consensus-ts(V;A;t;f)) y)
{}\mRightarrow{} (\mforall{}a:\{a:Id| (a \mmember{} A)\} . no\_repeats(consensus-rcv(V;A);filter(\mlambda{}x.rcv-vote?(x);y a))))
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