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Proof step 3 from proof inv-addn (previous step)

gstore1 = gstore, jro0 = jro, nx0 = nx, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, pmaxino ≠ 0, p_os < pmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, inv(gstore \ jro), inv(gstore0), refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), ri-inj(fi), ri-inj(fi0), pmaxino ≤ jmaxino, fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, ¬ dups(nx), jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ⟪gjournal_journal_addn#(ndx, jvalid0, fi, fi0, gstore0, pmaxino, p_os; ax, jvalid, jmaxino0, jro, gstore, nx, jvalid1; err)⟫ ( (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ ( err = ESUCCESS → # ax = # ndx ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx, gstore, jro) ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0)[ax, ndx] ∧ new(ax, nodes(gstore1 ↓, jro0))) ∧ (err ≠ ESUCCESS → abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0)))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
jvalid1 ↔ jvalid3, jvalid0 ↔ jvalid4, jvalid ↔ jvalid2, fi = fi1, fi0 = fi2, gstore1 = gstore, jro0 = jro, nx0 = nx, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, inv(gstore0), inv(gstore \ jro), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range fi2), ri-inj(fi1), ri-inj(fi2), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ ⟪let gndx = ?, jmaxino = ? in {gjournal_journal_transaction#(ndx, jmaxino0; ; gndx, jmaxino); gjournal_journal_allocate#(jmaxino, fi0, fi, gstore0, pmaxino, p_os; jvalid0, jro, gstore, nx, jvalid; err0); if err0 = ESUCCESS then index_add_gnds#(gndx, fi0, fi, jro, gstore0, nx, pmaxino, p_os; ax, gstore; jvalid, err0); if err0 = ESUCCESS then {jmaxino0 := jmaxino0 + # ndx; if jvalid1 then let err = ? in index_sync#(fi0, fi, jro, gstore, gstore0, nx, pmaxino, p_os; ; jvalid, err)} else jvalid0 := false}⟫ ( (jvalid0 ∧ 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 ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ ( err0 = ESUCCESS → # ax = # ndx ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx, gstore, jro) ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0)[ax, ndx] ∧ new(ax, nodes(gstore1 ↓, jro0))) ∧ (err0 ≠ ESUCCESS → abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro0))), pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: addn: ⊦ ;