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Proof step 10 from proof at-explicit (previous step)

# x1 = # lax1, # x0 = # lax0, st[n] = mkblock(x0 + a ' + x1, lax0 + @(m0, m1) ' + lax1, m2), inv-flashsize(x0 + a ' + x1, lax0 + @(m0, m1) ' + lax1), n ∈ st, @(n, m0, m1) ∈ st ⊦ st[@(n, m0, m1).lnum].list[pos(@(@(n, m0, m1).pos, @(n, m0, m1).size), st[@(n, m0, m1).lnum].ladrlist)] = a, dups(lax0 + lax1), dups(lax0), dups(lax1), @(m0, m1) ∈ lax0, @(m0, m1) ∈ lax1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# x1 = # lax1, # x0 = # lax0, st[n] = mkblock(x0 + a ' + x1, lax0 + @(m0, m1) ' + lax1, m2), inv-flashsize(x0 + a ' + x1, lax0 + @(m0, m1) ' + lax1), n ∈ st ⊦ (x0 + a ' + x1)[# lax0] = a, dups(lax0 + lax1), dups(lax0), dups(lax1), @(m0, m1) ∈ lax0, @(m0, m1) ∈ lax1

Rule argument

Additional information

Used simplifier rules: in: ⊦ adr ∈ st ↔ adr.lnum ∈ st ∧ @(adr.pos, adr.size) ∈ st[adr.lnum].ladrlist;% ⊦ ¬ ladr ∈ lax → (ladr ∈ ladr0 ' + lax ↔ ladr = ladr0); (s)% ⊦ ladr ∈ lax + lax0 ↔ ladr ∈ lax ∨ ladr ∈ lax0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ pos(ladr, ladr ' + lax) = 0; (s)% ⊦ ¬ ladr ∈ lax → pos(ladr, lax + lax0) = pos(ladr, lax0) + # lax; (s)% ⊦ mkblock(x, lax, m).ladrlist = lax; (s)% ⊦ mkblock(x, lax, m).list = x; (s)% ⊦ @(m, m0, m1).size = m1; (s)% ⊦ @(m, m0, m1).pos = m0; (s)% ⊦ @(m, m0, m1).lnum = m; (s)