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Proof step 13 from proof inv-alloc (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 ∈ st[n, mkblock(x0, lax0, m)] \ (ns -- n), inv-flashsize(x0, lax0) ∧ ¬ dups(lax0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: ablock-store-nat-store name: rem-write seq: ⊦ ¬ n ∈ ns → st[n, ablock] \ ns = (st \ ns)[n, ablock] subst: [ns, ablock, n, st] → [ns -- n, mkblock(x0, lax0, m), n, st] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)% ⊦ n ∈ st[n0, ablock] ↔ n = n0 ∨ n ∈ st; (ws) Used terms: ns -- n, mkblock(x0, lax0, m), n, st