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Proof step 30 from proof refine-add2 (previous step)

1 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr3 ' + ax0, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr3, nd2][ax0, nd1 '], 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(nd1.key, nd1), node-cons(nd2.key, nd2), nodes-cons(adr3 ' + ax0, nd2 ' + nd1 ', 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) ⊦ ∃ adr4, adr5. ¬ adr4 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr5 ∈ nodes(gstore ↓, jro0) ∧ adr4 ≠ adr5 ∧ ⟨adr0 := adr4, adr := adr5; fs := nodes(gstore ↓, jro0)[adr0, nd2][adr, nd1], log := (abs-log(nx, gstore ↓) + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ ax0[0] = adr ∧ ESUCCESS = err), jmaxino1 = 0, pmaxino = 0, dups(nx), dups(nx0), dups(ax0), adr3 ∈ nodes(gstore ↓, jro0), adr3 ∈ ax0

User applied rule constructor cut

And obtained the following new goals

Proof step 31:
1 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr3 ' + ax0, ax0 = adr1 + ax, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr3, nd2][ax0, nd1 '], 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(nd2.key, nd2), node-cons(nd1.key, nd1), nodes-cons(adr3 ' + ax0, nd2 ' + nd1 ', 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) ⊦ ∃ adr4, adr5. ¬ adr4 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr5 ∈ nodes(gstore ↓, jro0) ∧ adr4 ≠ adr5 ∧ ⟨adr0 := adr4, adr := adr5; fs := nodes(gstore ↓, jro0)[adr0, nd2][adr, nd1], log := (abs-log(nx, gstore ↓) + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ ax0[0] = adr ∧ ESUCCESS = err), jmaxino1 = 0, pmaxino = 0, dups(ax0), dups(nx0), dups(nx), adr3 ∈ ax0, adr3 ∈ 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)