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Proof step 40 from proof refine-add5 (previous step)

2 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr9 ' + adr1 ' + adr11 ' + ax0, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr9, nd7][adr1, nd6][adr11, nd1][ax0, nd5 ' + nd4 '], 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, adr1 ≠ adr11, adr9 ≠ adr1, adr9 ≠ adr11, jmaxino1 ≠ 0, pmaxino ≠ 0, 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(nd7.key, nd7), node-cons(nd6.key, nd6), node-cons(nd1.key, nd1), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), nodes-cons(adr9 ' + adr1 ' + adr11 ' + ax0, nd7 ' + nd6 ' + nd1 ' + nd5 ' + nd4 ', 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, ¬ dups(nx), ¬ dups(nx0), ¬ dups(ax0), ¬ adr11 ∈ nodes(gstore ↓, jro0), ¬ adr1 ∈ ax0, ¬ adr9 ∈ nodes(gstore ↓, jro0), ¬ adr9 ∈ ax0, ¬ adr1 ∈ nodes(gstore ↓, jro0), ¬ adr11 ∈ ax0, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ∃ adr2, adr3, adr4, adr5, adr10. ¬ adr2 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr3 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr4 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr5 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr10 ∈ nodes(gstore ↓, jro0) ∧ adr2 ≠ adr3 ∧ adr2 ≠ adr4 ∧ adr2 ≠ adr5 ∧ adr2 ≠ adr10 ∧ adr3 ≠ adr4 ∧ adr3 ≠ adr5 ∧ adr3 ≠ adr10 ∧ adr4 ≠ adr5 ∧ adr4 ≠ adr10 ∧ adr5 ≠ adr10 ∧ ⟨adr8 := adr2, adr7 := adr3, adr6 := adr4, adr0 := adr5, adr := adr10; fs := nodes(gstore ↓, jro0)[adr8, nd7][adr7, nd6][adr6, nd1][adr0, nd5][adr, nd4], log := ((((abs-log(nx, gstore ↓) + adr8 ') + adr7 ') + adr6 ') + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ ( log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr9 = adr8 ∧ adr1 = adr7 ∧ adr11 = adr6 ∧ ax0[0] = adr0 ∧ ax0[1] = adr ∧ ESUCCESS = err)

User applied rule constructor cut

And obtained the following new goals

Proof step 41:
2 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr9 ' + adr1 ' + adr11 ' + ax0, ax0 = adr12 + ax1, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr9, nd7][adr1, nd6][adr11, nd1][ax0, nd5 ' + nd4 '], 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(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd1.key, nd1), node-cons(nd6.key, nd6), node-cons(nd7.key, nd7), nodes-cons(adr9 ' + adr1 ' + adr11 ' + ax0, nd7 ' + nd6 ' + nd1 ' + nd5 ' + nd4 ', 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) ⊦ ∃ adr2, adr3, adr4, adr5, adr10. ¬ adr2 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr3 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr4 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr5 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr10 ∈ nodes(gstore ↓, jro0) ∧ adr2 ≠ adr3 ∧ adr2 ≠ adr4 ∧ adr2 ≠ adr5 ∧ adr2 ≠ adr10 ∧ adr3 ≠ adr4 ∧ adr3 ≠ adr5 ∧ adr3 ≠ adr10 ∧ adr4 ≠ adr5 ∧ adr4 ≠ adr10 ∧ adr5 ≠ adr10 ∧ ⟨adr8 := adr2, adr7 := adr3, adr6 := adr4, adr0 := adr5, adr := adr10; fs := nodes(gstore ↓, jro0)[adr8, nd7][adr7, nd6][adr6, nd1][adr0, nd5][adr, nd4], log := ((((abs-log(nx, gstore ↓) + adr8 ') + adr7 ') + adr6 ') + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ ( log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr9 = adr8 ∧ adr1 = adr7 ∧ adr11 = adr6 ∧ ax0[0] = adr0 ∧ ax0[1] = adr ∧ ESUCCESS = err), adr1 = adr11, adr9 = adr1, adr9 = adr11, jmaxino1 = 0, pmaxino = 0, dups(nx), dups(nx0), dups(ax0), adr11 ∈ nodes(gstore ↓, jro0), adr1 ∈ ax0, adr9 ∈ nodes(gstore ↓, jro0), adr9 ∈ ax0, adr1 ∈ nodes(gstore ↓, jro0), adr11 ∈ ax0

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)