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Proof step 10 from proof inv-alloc (previous step)

(st[n, mkblock(x, lax, m)] \ (ns -- n))[n] = mkblock(x0, lax0, m0), n ∈ st[n, mkblock(x, lax, m)] \ (ns -- n) → inv-flashsize(x0, lax0) ∧ ¬ dups(lax0), ∀ 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 -- n, inv-flashsize(x, lax) ∧ ¬ dups(lax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ 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 ∈ st[n, mkblock(x0, lax0, m)] \ (ns -- n), inv-flashsize(x0, lax0) ∧ ¬ dups(lax0)

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)%⊦ mkblock(x, lax, m) = mkblock(x0, lax0, m0) ↔ x = x0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ st[n, ablock][n] = ablock; (s)% ⊦ ¬ n ∈ ns → (st \ ns)[n] = st[n]; (s)