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Proof step 4 from proof at-explicit-diff (previous step)

# x0 = # lax0, st[n] = mkblock(x0 + a ' + x1, lax0 + @(m0, m1) ' + lax1, m2), n ∈ st, n ∈ st \ ns → # (st \ ns)[n].list = # (st \ ns)[n].ladrlist ∧ inv-flashsize((st \ ns)[n].list, (st \ ns)[n].ladrlist) ∧ ¬ dups((st \ ns)[n].ladrlist) ⊦ st[@(n, m0, m1)] = a, n ∈ ns

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# x0 = # lax0, # x1 = # lax1, st[n] = mkblock(x0 + a ' + x1, lax0 + @(m0, m1) ' + lax1, m2), inv-flashsize(x0 + a ' + x1, lax0 + @(m0, m1) ' + lax1), n ∈ st ⊦ st[@(n, m0, m1)] = a, dups(lax1), dups(lax0), dups(lax0 + lax1), @(m0, m1) ∈ lax1, @(m0, m1) ∈ lax0, n ∈ ns

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)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ #(ladr ' + lax) = (# lax)+1; (s)% ⊦ #(lax + lax0) = # lax + # lax0; (s)% ⊦ mkblock(x, lax, m).ladrlist = lax; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ m +1 = m + 1; (s)% ⊦ #(a ' + x) = (# x)+1; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ mkblock(x, lax, m).list = x; (s)% ⊦ ¬ n ∈ ns → (st \ ns)[n] = st[n]; (s)% ⊦ n ∈ st \ ns ↔ n ∈ st ∧ ¬ n ∈ ns; (ws)