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Proof step 7 from proof inv-reduce (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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), n ∈ ns ∨ inv-flashsize(x, lax) ∧ ¬ dups(lax) ⊦ n0 ∈ ns, inv-flashsize(st[n, mkblock(x, lax, m)][n0].list, st[n, mkblock(x, lax, m)][n0].ladrlist) ∧ ¬ dups(st[n, mkblock(x, lax, m)][n0].ladrlist)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n ∈ ns → (st \ ns)[n] = st[n]; (s)% ⊦ n ∈ st \ ns ↔ n ∈ st ∧ ¬ n ∈ ns; (ws)