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Proof step 32 from proof refine-add3 (previous step)

2 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr5 ' + ax0, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr5, nd3][ax0, nd0 ' + nd2 '], 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?, jro1 < jmaxino1, p_os < pmaxino, ri.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), inv(gstore1 \ jro), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), new(ax0, nodes(gstore ↓, jro0)), node-cons(nd3.key, nd3), node-cons(nd0.key, nd0), node-cons(nd2.key, nd2), nodes-cons(adr5 ' + ax0, nd3 ' + nd0 ' + nd2 ', gstore1, jro), 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, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ∃ adr6, adr7, adr8. ¬ adr6 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr7 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr8 ∈ nodes(gstore ↓, jro0) ∧ adr6 ≠ adr7 ∧ adr6 ≠ adr8 ∧ adr7 ≠ adr8 ∧ ⟨adr4 := adr6, adr0 := adr7, adr := adr8; fs := nodes(gstore ↓, jro0)[adr4, nd3][adr0, nd0][adr, nd2], log := ((abs-log(nx, gstore ↓) + adr4 ') + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ ( log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr5 = adr4 ∧ ax0[0] = adr0 ∧ ax0[1] = adr ∧ ESUCCESS = err), jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx), dups(ax0), adr5 ∈ nodes(gstore ↓, jro0), adr5 ∈ ax0

User applied rule constructor cut

And obtained the following new goals

Proof step 33:
2 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr5 ' + ax0, ax0 = adr1 + ax, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr5, nd3][ax0, 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, 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(ax0, nodes(gstore ↓, jro0)), node-cons(nd2.key, nd2), node-cons(nd0.key, nd0), node-cons(nd3.key, nd3), nodes-cons(adr5 ' + ax0, 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, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ∃ adr6, adr7, adr8. ¬ adr6 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr7 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr8 ∈ nodes(gstore ↓, jro0) ∧ adr6 ≠ adr7 ∧ adr6 ≠ adr8 ∧ adr7 ≠ adr8 ∧ ⟨adr4 := adr6, adr0 := adr7, adr := adr8; fs := nodes(gstore ↓, jro0)[adr4, nd3][adr0, nd0][adr, nd2], log := ((abs-log(nx, gstore ↓) + adr4 ') + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ ( log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr5 = adr4 ∧ ax0[0] = adr0 ∧ ax0[1] = adr ∧ ESUCCESS = err), jmaxino1 = 0, pmaxino = 0, dups(ax0), dups(nx), dups(nx0), adr5 ∈ ax0, adr5 ∈ nodes(gstore ↓, jro0)

Rule argument

var: ax0

Additional information

Used simplifier rules: address-list freely generated by [], +;;% ⊦ ax + [] = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ # [] = 0; (s)