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Proof step 8 from proof inv-alloc (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
(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) ⊦ inv-flashsize(x, lax) ∧ ¬ dups(lax)

Rule argument

spec: ablock name: elim seq: ⊦ (x = ablock.list ∧ lax = ablock.ladrlist) ∧ m = ablock.ref-size ↔ ablock = mkblock(x, lax, m) subst: [ablock, x, lax, m] → [(st[n, mkblock(x, lax, m)] \ (ns -- n))[n], x0, lax0, m0]

Additional information

Used simplifier rules: ⊦ (x = ablock.list ∧ lax = ablock.ladrlist) ∧ m = ablock.ref-size ↔ ablock = mkblock(x, lax, m); (elim) Used terms: (st[n, mkblock(x, lax, m)] \ (ns -- n))[n], x0, lax0, m0