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Proof step 49 from proof refine-get (previous step)

remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-inj(ri), ri-inj(fi1), @(m, m0, m1) ∈ gstore2, m ∈ jro0, @(m, m0, m1) ∈ nodes(gstore2 ↓, jro0), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ # jro0 = 0, jmaxino = 0, jro0 = ∅, pmaxino = 0, dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: gjournal-abs name: nodes-gstore-in seq: ⊦ adr ∈ nodes(gstore, ginval) ↔ ¬ ¬(adr ∈ gstore ∧ ¬ adr.lnum ∈ ginval) subst: [ginval, gstore, adr] → [jro0, gstore2 ↓, @(m, m0, m1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ @(m0, m1, m2) ∈ gstore ↓ ↔ m0 ∈ gstore ∧ @(m1, m2) ∈ gstore ↓[m0].ladrlist; (ws)% ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓; (s)% ⊦ @(m, m0, m1).lnum = m; (s) Used terms: jro0, gstore2 ↓, @(m, m0, m1)