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Proof step 25 from proof refine-add2 (previous step)

# ax = 2, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax, ax = adr3 + ax0, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[ax, nd2 ' + 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(ax, nodes(gstore ↓, jro0)), node-cons(nd2.key, nd2), node-cons(nd1.key, nd1), nodes-cons(ax, 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) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; adr0 := ?, adr := ?; jvalid := ?⟩ ( abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ nodes(gstore ↓, jro0) = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ ax[1] = adr ∧ ESUCCESS = err), ⟨choose adr1, adr2 with new(adr1 ' + adr2 ', fs) ∧ ¬ dups(adr1 ' + adr2 ') in {adr0 := adr1, adr := adr2; fs := fs[adr0, nd2][adr, nd1], log := (log + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC; jvalid := ?⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ ax[1] = adr ∧ ESUCCESS = err), ax = [], jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx), dups(ax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
1 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr3 ' + ax0, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), 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, 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)), 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, ¬ dups(nx), ¬ dups(nx0), ¬ dups(ax0), ¬ adr3 ∈ nodes(gstore ↓, jro0), ¬ adr3 ∈ ax0, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; adr0 := ?, adr := ?; jvalid := ?⟩ ( abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ nodes(gstore ↓, jro0) = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ ax0[0] = adr ∧ ESUCCESS = err), ⟨choose adr1, adr2 with new(adr1 ' + adr2 ', fs) ∧ ¬ dups(adr1 ' + adr2 ') in {adr0 := adr1, adr := adr2; fs := fs[adr0, nd2][adr, nd1], log := (log + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC; jvalid := ?⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ ax0[0] = adr ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: n ≠ 0 ⊦ (adr ' + ax)[(* n)] = ax[n -1]; (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)% ⊦ adr ' + ax ≠ []; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n0 < n ⊦ (* n) = m0 + (* n0) ↔ n - n0 = m0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ #(adr ' + ax) = (# ax)+1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ fs[adr ' + ax, nd ' + ndx] = fs[adr, nd][ax, ndx]; (s)% ⊦ adr + ax = adr ' + ax; (s)