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Proof step 8 from proof inv-add5 (previous step)

jvalid2 ↔ jvalid1, fi3 = fi2, fi4 = fi1, gstore = gstore, gstore2 = gstore0, gstore3 = gstore, jmaxino2 = jmaxino1, jro = jro, jro1 = jro, ndx0 = nd3 ' + nd2 ' + nd1 ' + nd0 ' + nd ', nx = nx, nx1 = nx, p_os0 = p_os, pmaxino0 = pmaxino, 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), inv-journal(nx, gstore, gstore0, jro), 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) ⊦ [gjournal_journal_addn# (nd3 ' + nd2 ' + nd1 ' + nd0 ' + nd ', jvalid1, fi2, fi1, gstore0, pmaxino, p_os; ax, jvalid4, jmaxino, jro, gstore, nx, jvalid; err)] ( (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi3.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi3) ∧ inv-journal(nx, gstore, gstore2, jro) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ dom gstore3 ⊆ dom gstore ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore3 = ∅ ∧ ( err = ESUCCESS → # ax = # ndx0 ∧ ¬ dups(ax) ∧ nodes-cons(ax, ndx0, gstore, jro) ∧ abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) + ax ∧ nodes(gstore ↓, jro) = nodes(gstore3 ↓, jro1)[ax, ndx0] ∧ 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 {adr3 := ax[0]; adr2 := ax[1]; adr1 := ax[2]; adr0 := ax[3]; adr := ax[4]}⟫ ( (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)), pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
gstore3 = gstore, jro1 = jro, nx1 = nx, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, pmaxino ≠ 0, fi1.inos < pmaxino, fi2.inos < jmaxino1, 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 ≤ jmaxino1, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore, ¬ dups(nx), jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro) ⊦ [gjournal_journal_addn# (nd3 ' + nd2 ' + nd1 ' + nd0 ' + nd ', jvalid1, fi2, fi1, gstore0, pmaxino, p_os; 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 = 5 ∧ ¬ dups(ax) ∧ nodes-cons(ax, nd3 ' + nd2 ' + nd1 ' + nd0 ' + nd ', gstore, jro) ∧ abs-log(nx, gstore ↓) = abs-log(nx1, gstore3 ↓) + ax ∧ nodes(gstore ↓, jro) = nodes(gstore3 ↓, jro1)[ax, nd3 ' + nd2 ' + nd1 ' + 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 {adr3 := ax[0]; adr2 := ax[1]; adr1 := ax[2]; adr0 := ax[3]; adr := ax[4]}⟫ (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ # nd ' = 0 +1; (s)% ⊦ #(nd ' + ndx) = (# ndx)+1; (s)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)