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Proof step 10 from proof inv-add2 (previous step)

gstore3 = gstore, jro1 = jro, nx1 = nx, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore \ jro), inv(gstore0), refsize-cons(gstore, range fi2), refsize-cons(gstore0, range fi1), ri-inj(fi2), ri-inj(fi1), pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ∀ ax, jvalid4, jmaxino, jro, gstore, nx, jvalid, err. (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi2.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi2) ∧ inv(gstore \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore3 ⊆ dom gstore ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore3 = ∅ ∧ ( err = ESUCCESS → # ax = 2 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd0 ' + nd ', gstore, jro) ∧ abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) + ax ∧ nodes(gstore ↓, jro) = nodes(gstore3 ↓, jro1)[ax, nd0 ' + nd '] ∧ new(ax, nodes(gstore3 ↓, jro1))) ∧ (err ≠ ESUCCESS → abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) ∧ nodes(gstore ↓, jro) = nodes(gstore3 ↓, jro1)) → ⟪if err = ESUCCESS then {adr0 := ax[0]; adr := ax[1]}⟫ (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)), pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
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, pmaxino ≠ 0, 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, ¬ dups(nx), ¬ dups(nx0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro0), err = ESUCCESS → # ax = 2 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd0 ' + nd ', gstore1, jro0) ∧ abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax ∧ nodes(gstore1 ↓, jro0) = nodes(gstore ↓, jro)[ax, 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⌋ ⊦ ⟪if err = ESUCCESS then {adr0 := ax[0]; adr := ax[1]}⟫ (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro0))

Rule argument

Additional information

Used simplifier rules: sub-trans: ⊦ ns ⊆ ns0 ∧ ns0 ⊆ ns1 → ns ⊆ ns1; (forward) from specification set-basic[nat-set]