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Proof step 35 from proof refine-add3 (previous step)

1 = # ax, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr5 ' + adr1 ' + ax, ax = adr7 + ax0, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr5, nd3][adr1, nd0][ax, 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(ax, nodes(gstore ↓, jro0)), node-cons(nd2.key, nd2), node-cons(nd0.key, nd0), node-cons(nd3.key, nd3), nodes-cons(adr5 ' + adr1 ' + 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, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ∃ adr2, adr3, adr6. ¬ adr2 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr3 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr6 ∈ nodes(gstore ↓, jro0) ∧ adr2 ≠ adr3 ∧ adr2 ≠ adr6 ∧ adr3 ≠ adr6 ∧ ⟨adr4 := adr2, adr0 := adr3, adr := adr6; 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 ∧ adr1 = adr0 ∧ ax[0] = adr ∧ ESUCCESS = err), adr5 = adr1, jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx), dups(ax), adr1 ∈ nodes(gstore ↓, jro0), adr5 ∈ nodes(gstore ↓, jro0), adr5 ∈ ax, adr1 ∈ ax

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr5 ' + adr1 ' + adr7 ', nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr5, nd3][adr1, nd0][adr7, 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, adr1 ≠ adr7, adr5 ≠ adr7, adr5 ≠ adr1, 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)), node-cons(nd2.key, nd2), node-cons(nd0.key, nd0), node-cons(nd3.key, nd3), nodes-cons(adr5 ' + adr1 ' + adr7 ', 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), adr7 ∈ abs-log(nx0, gstore1 ↓), pmaxino ≤ jmaxino1, dom gstore ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ri.lebs ⊆ dom gstore1, ¬ dups(nx0), ¬ dups(nx), ¬ adr1 ∈ nodes(gstore ↓, jro0), ¬ adr5 ∈ nodes(gstore ↓, jro0), ¬ adr7 ∈ nodes(gstore ↓, jro0), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ∃ adr2, adr3, adr6. ¬ adr2 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr3 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr6 ∈ nodes(gstore ↓, jro0) ∧ adr2 ≠ adr3 ∧ adr2 ≠ adr6 ∧ adr3 ≠ adr6 ∧ ⟨adr4 := adr2, adr0 := adr3, adr := adr6; 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 ∧ adr1 = adr0 ∧ adr7 = adr ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: in-15: ⊦ ax + adr ' = ax0 → adr ∈ ax0; (forward) from specification list[address-list-set]% ⊦ ¬ dups([]); (s)% ⊦ ¬ adr ∈ []; (s)% ⊦ new([], fs); (s)% ⊦ fs[adr ', nd '] = fs[adr, nd]; (s)% ⊦ ax + [] = ax; (s)% ⊦ (adr ' + ax)[0] = adr; (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ adr ∈ adr0 ' + ax ↔ ¬(adr ≠ adr0 ∧ ¬ adr ∈ ax); (ss)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # ax = 0 ↔ ax = []; (s)% ⊦ 1 = m + 1 ↔ m = 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ #(adr ' + ax) = (# ax)+1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr + ax = adr ' + ax; (s)