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Proof step 34 from proof refine-add1 (previous step)

abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr0, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0), 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, 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)), node-cons(nd.key, nd), 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, ⌊err⌋ , ¬ dups(nx0), ¬ dups(nx), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ⟨aubifs_core_journal_add1#(nd, ri, fi1, jro1.keys, p_os.keys; adr0, fs, log; jvalid5, err0)⟩ (log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid5 → jvalid) ∧ adr = adr0 ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 35:
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr0, adr1 = adr0, fi = fi1, fo = p_os.keys, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0), 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)), node-cons(nd.key, nd), 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, ⌊err1⌋ , 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(nd.key, nd) then { choose adr1 with new(adr1 ', fs) ∧ ¬ dups(adr1 ') in {adr := adr1; fs[adr] := nd, log := log + adr, err := ESUCCESS} ifnone err := ENOSPC or {fail#(; ; err); adr := ?}; jvalid := ?} else abort⟩ (log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr1 = adr ∧ err1 = err), jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_journal_add1# (ND1, RI, FI, RO, FO; ADR1, FS, LOG; CSYNCED, ERR) {if ri-cons(RI, FS) ∧ node-cons(ND1.key, ND1) then { choose adr1 with new(adr1 ', FS) ∧ ¬ dups(adr1 ') in {ADR1 := adr1; FS[ADR1] := ND1, LOG := LOG + ADR1, ERR := ESUCCESS} ifnone ERR := ENOSPC or {fail#(; ; ERR); ADR1 := ?}; CSYNCED := ?} else abort };