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Proof step 13 from proof inv-add4 (previous step)

err = ESUCCESS, remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro0, dom gstore0 ∪ elems nx = dom gstore ∪ jro, 0 < # ax, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(gstore1 \ jro0), inv(gstore0), inv(gstore \ jro), refsize-cons(gstore1, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range fi2), ri-inj(fi1), ri-inj(fi2), pmaxino ≤ jmaxino1, dom gstore ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore, fi2.lebs ⊆ dom gstore1, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro0), err = ESUCCESS → # ax = 4 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd2 ' + nd1 ' + nd0 ' + nd ', gstore1, jro0) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro)[ax, nd2 ' + nd1 ' + nd0 ' + nd '] ∧ new(ax, nodes(gstore ↓, jro)), err ≠ ESUCCESS → abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro), jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪adr1 := ax[1]; adr0 := ax[2]; adr := ax[3]⟫ (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro0)), pmaxino = 0, dups(nx0), dups(nx)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 14:
err = ESUCCESS, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx0 ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro0, 1 < # ax, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, 0 < # ax, inv(gstore \ jro), inv(gstore0), inv(gstore1 \ jro0), refsize-cons(gstore, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore1, range fi2), ri-inj(fi2), ri-inj(fi1), pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, dom gstore ⊆ dom gstore1, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), err ≠ ESUCCESS → abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro), err = ESUCCESS → # ax = 4 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd2 ' + nd1 ' + nd0 ' + nd ', gstore1, jro0) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro)[ax, nd2 ' + nd1 ' + nd0 ' + nd '] ∧ new(ax, nodes(gstore ↓, jro)), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro0), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪adr0 := ax[2]; adr := ax[3]⟫ (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro0)), pmaxino = 0, dups(nx), dups(nx0)

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ # ax = 0 ↔ ax = []; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)