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Proof step 43 from proof refine-add5 (previous step)

1 = # ax1, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr9 ' + adr1 ' + adr11 ' + adr12 ' + ax1, ax1 = adr13 + ax2, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr9, nd7][adr1, nd6][adr11, nd1][adr12, nd5][ax1, 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(ax1, 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 ' + adr12 ' + ax1, 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 ∧ adr12 = adr0 ∧ ax1[0] = adr ∧ ESUCCESS = err), adr1 = adr11, adr1 = adr12, adr11 = adr12, adr9 = adr11, adr9 = adr1, adr9 = adr12, jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx), dups(ax1), adr12 ∈ nodes(gstore ↓, jro0), adr11 ∈ ax1, adr1 ∈ nodes(gstore ↓, jro0), adr9 ∈ ax1, adr9 ∈ nodes(gstore ↓, jro0), adr1 ∈ ax1, adr11 ∈ nodes(gstore ↓, jro0), adr12 ∈ ax1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr9 ' + adr1 ' + adr11 ' + adr12 ' + adr13 ', nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr9, nd7][adr1, nd6][adr11, nd1][adr12, nd5][adr13, 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, adr1 ≠ adr13, adr1 ≠ adr11, adr1 ≠ adr12, adr11 ≠ adr13, adr11 ≠ adr12, adr12 ≠ adr13, adr9 ≠ adr13, adr9 ≠ adr11, adr9 ≠ adr1, adr9 ≠ adr12, 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(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 ' + adr12 ' + adr13 ', 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), adr13 ∈ 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), ¬ adr12 ∈ nodes(gstore ↓, jro0), ¬ adr1 ∈ nodes(gstore ↓, jro0), ¬ adr9 ∈ nodes(gstore ↓, jro0), ¬ adr11 ∈ nodes(gstore ↓, jro0), ¬ adr13 ∈ nodes(gstore ↓, jro0), 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 ∧ adr12 = adr0 ∧ adr13 = 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)