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Proof step 19 from proof refine-add3 (previous step)

# ax = 3, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[ax, nd3 ' + nd0 ' + nd2 '], remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, ax ≠ [], jmaxino1 ≠ 0, pmaxino ≠ 0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino1, p_os < pmaxino, jro1 < jmaxino1, inv(gstore1 \ jro), inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), new(ax, nodes(gstore ↓, jro0)), node-cons(nd2.key, nd2), node-cons(nd0.key, nd0), node-cons(nd3.key, nd3), nodes-cons(ax, nd3 ' + nd0 ' + nd2 ', gstore1, jro), refsize-cons(gstore1, range ri), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino1, dom gstore ⊆ dom gstore1, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, ri.lebs ⊆ dom gstore1, ¬ dups(nx0), ¬ dups(nx), ¬ dups(ax), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ⟨aubifs_core_journal_add3#(nd3, nd0, nd2, ri, fi1, jro1.keys, p_os.keys; adr5, adr2, adr4, fs, log; jvalid5, err0)⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid5 → jvalid) ∧ ax.head = adr5 ∧ ax[1] = adr2 ∧ ax[2] = adr4 ∧ ESUCCESS = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 20:
# ax = 3, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + ax, adr = adr1, adr0 = adr2, adr4 = adr5, fi = fi1, fo = p_os.keys, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nd = nd2, nd1 = nd3, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[ax, nd3 ' + nd0 ' + nd2 '], remove-refsize0(gstore0) = gstore0, ro = jro1.keys, elems nx ∩ jro0 = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore = ∅, elems nx0 ∩ jro = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, dom gstore0 ∪ elems nx0 = dom gstore1 ∪ jro, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino1, p_os < pmaxino, ri.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), inv(gstore1 \ jro), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), new(ax, nodes(gstore ↓, jro0)), node-cons(nd3.key, nd3), node-cons(nd0.key, nd0), node-cons(nd2.key, nd2), nodes-cons(ax, nd3 ' + nd0 ' + nd2 ', gstore1, jro), refsize-cons(gstore, range ri), refsize-cons(gstore0, range fi1), refsize-cons(gstore1, range ri), ri-cons(ri, nodes(gstore ↓, jro0)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino1, ri.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, dom gstore ⊆ dom gstore1, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟨if ri-cons(ri, fs) ∧ node-cons(nd1.key, nd1) ∧ node-cons(nd0.key, nd0) ∧ node-cons(nd.key, nd) then { choose adr1, adr2, adr3 with new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ') in {adr4 := adr1, adr0 := adr2, adr := adr3; fs := fs[adr4, nd1][adr0, nd0][adr, nd], log := ((log + adr4) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC or {fail#(; ; err); adr4 := ?, adr0 := ?, adr := ?}; jvalid := ?} else abort⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ ax.head = adr4 ∧ ax[1] = adr0 ∧ ax[2] = adr ∧ ESUCCESS = err), ax = [], jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx), dups(ax)

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_journal_add3# (ND1, ND2, ND3, RI, FI, RO, FO ; ADR1, ADR2, ADR3, FS, LOG ; CSYNCED, ERR ) {if ri-cons(RI, FS) ∧ node-cons(ND1.key, ND1) ∧ node-cons(ND2.key, ND2) ∧ node-cons(ND3.key, ND3) then { choose adr1, adr2, adr3 with new(adr1 ' + (adr2 ' + adr3), FS) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ') in {ADR1 := adr1, ADR2 := adr2, ADR3 := adr3; FS := FS[ADR1, ND1][ADR2, ND2][ADR3, ND3], LOG := ((LOG + ADR1) + ADR2) + ADR3, ERR := ESUCCESS} ifnone ERR := ENOSPC or {fail#(; ; ERR); ADR1 := ?, ADR2 := ?, ADR3 := ?}; CSYNCED := ?} else abort };