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Proof step 15 from proof inv-alloc (previous step)

inv-flashsize(x, lax), ∀ n0. n0 ∈ st \ ns → # (st \ ns)[n0].list = # (st \ ns)[n0].ladrlist ∧ inv-flashsize((st \ ns)[n0].list, (st \ ns)[n0].ladrlist) ∧ ¬ dups((st \ ns)[n0].ladrlist) ⊦ dups(lax), ∀ n0. n0 ∈ st[n, mkblock(x, lax, m)] \ (ns -- n) → inv-flashsize((st[n, mkblock(x, lax, m)] \ (ns -- n))[n0].list, (st[n, mkblock(x, lax, m)] \ (ns -- n))[n0].ladrlist) ∧ ¬ dups((st[n, mkblock(x, lax, m)] \ (ns -- n))[n0].ladrlist)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
inv-flashsize(x, lax), n0 ∈ st[n, mkblock(x, lax, m)], ∀ n0. n0 ∈ st \ ns → # (st \ ns)[n0].list = # (st \ ns)[n0].ladrlist ∧ inv-flashsize((st \ ns)[n0].list, (st \ ns)[n0].ladrlist) ∧ ¬ dups((st \ ns)[n0].ladrlist), n0 = n ∨ ¬ n0 ∈ ns ⊦ dups(lax), inv-flashsize((st[n, mkblock(x, lax, m)] \ (ns -- n))[n0].list, (st[n, mkblock(x, lax, m)] \ (ns -- n))[n0].ladrlist) ∧ ¬ dups((st[n, mkblock(x, lax, m)] \ (ns -- n))[n0].ladrlist)

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)% ⊦ n ∈ st \ ns ↔ n ∈ st ∧ ¬ n ∈ ns; (ws)