[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 13 from proof inv-add3 (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 = 3 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd1 ' + nd0 ' + nd ', gstore1, jro0) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro)[ax, 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⌋ ⊦ ⟪adr0 := ax[1]; adr := ax[2]⟫ (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 = 3 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd1 ' + nd0 ' + nd ', gstore1, jro0) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro)[ax, nd1 ' + nd0 ' + nd '] ∧ new(ax, nodes(gstore ↓, jro)), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro0), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪adr := ax[2]⟫ (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)