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Proof step 23 from proof refine-add1 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr0 ', fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr0, nd], 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, 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)), node-cons(nd.key, nd), nodes-cons(adr0 ', nd ', 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), adr0 ∈ abs-log(nx0, gstore1 ↓), pmaxino ≤ jmaxino1, ri.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, dom gstore ⊆ dom gstore1, ¬ dups(nx0), ¬ dups(nx), ¬ adr0 ∈ nodes(gstore ↓, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟨choose adr1 with new(adr1 ', fs) ∧ ¬ dups(adr1 ') in {adr := adr1; fs[adr] := nd, log := log + adr, err := ESUCCESS} ifnone err := ENOSPC; jvalid := ?⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr0 = adr ∧ ESUCCESS = err), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; adr := ?; jvalid := ?⟩ ( abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ nodes(gstore ↓, jro0) = nodes(gstore ↓, jro0)[adr, nd] ∧ (jvalid → jvalid1) ∧ adr0 = 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)% ⊦ 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% ⊦ # 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)