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Proof step 17 from proof inv-valid-adrs (previous step)

# x = # lax, st[m] = mkblock(x, lax, m1), inv-flashsize(x, lax), m ∈ st, @(m, m0, 0) ∈ as, as ⊆ dom nodes(st), ∃ lax0, lax1. lax = lax0 + (@(m0, 0) + lax1) ⊦ # as = 0, as = ∅, dups(lax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# x = # lax1 + # lax0 + 1, st[m] = mkblock(x, lax1 + @(m0, 0) ' + lax0, m1), inv-flashsize(x, lax1 + @(m0, 0) ' + lax0), @(m, m0, 0) ∈ as, m ∈ st, as ⊆ dom nodes(st) ⊦ # as = 0, as = ∅, dups(lax1 + lax0), dups(lax1), dups(lax0), @(m0, 0) ∈ lax1, @(m0, 0) ∈ lax0

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]%⊦ dups(lax + ladr ' + lax0) ↔ ladr ∈ lax ∨ ladr ∈ lax0 ∨ dups(lax + lax0); (ws)% ⊦ m +1 = m + 1; (s)% ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ ladr + lax = ladr ' + lax; (s)