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Proof step 18 from proof refine-add3 (previous step)

adr = adr4, adr0 = adr2, adr1 = adr5, err = ESUCCESS, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx0 ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro, jro1.keys.inodes?, p_os.keys.inodes?, 2 < # ax, 0 < # ax, jro1 < jmaxino1, p_os < pmaxino, ri.inos < jmaxino1, fi1.inos < pmaxino, 1 < # ax, inv(gstore \ jro0), inv(gstore0), inv(gstore1 \ jro), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), node-cons(nd3.key, nd3), node-cons(nd0.key, nd0), node-cons(nd2.key, nd2), refsize-cons(gstore, range ri), refsize-cons(gstore0, range fi1), refsize-cons(gstore1, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino1, ri.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, dom gstore ⊆ dom gstore1, jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), err ≠ ESUCCESS → abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) ∧ nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0), err = ESUCCESS → # ax = 3 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd3 ' + nd0 ' + nd2 ', gstore1, jro) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[ax, nd3 ' + nd0 ' + nd2 '] ∧ new(ax, nodes(gstore ↓, jro0)), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨aubifs_core_journal_add3#(nd3, nd0, nd2, ri, fi1, jro1.keys, p_os.keys; adr5, adr2, adr4, fs, log; jvalid5, err0)⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid5 → jvalid) ∧ ax[0] = adr5 ∧ ax[1] = adr2 ∧ ax[2] = adr4 ∧ err = err0), jmaxino1 = 0, pmaxino = 0, dups(nx), dups(nx0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# ax = 3, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[ax, nd3 ' + nd0 ' + nd2 '], remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, ax ≠ [], jmaxino1 ≠ 0, pmaxino ≠ 0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino1, p_os < pmaxino, jro1 < jmaxino1, inv(gstore1 \ jro), inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), new(ax, nodes(gstore ↓, jro0)), node-cons(nd2.key, nd2), node-cons(nd0.key, nd0), node-cons(nd3.key, nd3), nodes-cons(ax, nd3 ' + nd0 ' + nd2 ', gstore1, jro), refsize-cons(gstore1, range ri), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino1, dom gstore ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ri.lebs ⊆ dom gstore1, ¬ dups(nx0), ¬ dups(nx), ¬ dups(ax), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ⟨aubifs_core_journal_add3#(nd3, nd0, nd2, ri, fi1, jro1.keys, p_os.keys; adr5, adr2, adr4, fs, log; jvalid5, err0)⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid5 → jvalid) ∧ ax.head = adr5 ∧ ax[1] = adr2 ∧ ax[2] = adr4 ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ ax ≠ [] → ax[0] = ax.head; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ # ax = 0 ↔ ax = []; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)