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Proof step 51 from proof refine-add5 (previous step)

abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr8, adr0 = adr6, adr1 = adr4, adr12 = adr10, adr13 = adr9, 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(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd1.key, nd1), node-cons(nd6.key, nd6), node-cons(nd7.key, nd7), 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_add5#(nd7, nd6, nd1, nd5, nd4, ri, fi1, jro1.keys, p_os.keys; adr9, adr10, adr4, adr6, adr8, fs, log; jvalid5, err0)⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid5 → jvalid) ∧ adr13 = adr9 ∧ adr12 = adr10 ∧ adr1 = adr4 ∧ adr0 = adr6 ∧ adr = adr8 ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 52:
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr5, adr0 = adr11, adr1 = adr4, adr12 = adr10, adr13 = adr9, adr2 = adr11, adr3 = adr5, adr6 = adr4, adr7 = adr10, adr8 = adr9, fi = fi1, fo = p_os.keys, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nd = nd4, nd0 = nd5, nd2 = nd6, nd3 = nd7, 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(nd7.key, nd7), node-cons(nd6.key, nd6), node-cons(nd1.key, nd1), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), 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(nd3.key, nd3) ∧ node-cons(nd2.key, nd2) ∧ node-cons(nd1.key, nd1) ∧ node-cons(nd0.key, nd0) ∧ node-cons(nd.key, nd) then { choose adr1, adr2, adr3, adr4, adr5 with new(adr1 ' + adr2 ' + adr3 ' + (adr4 ' + adr5), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ' + adr5 ') in {adr8 := adr1, adr7 := adr2, adr6 := adr3, adr0 := adr4, adr := adr5; fs := fs[adr8, nd3][adr7, nd2][adr6, nd1][adr0, nd0][adr, nd], log := ((((log + adr8) + adr7) + adr6) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC or {fail#(; ; err); adr8 := ?, adr7 := ?, adr6 := ?, adr0 := ?, adr := ?}; jvalid := ?} else abort⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr13 = adr8 ∧ adr12 = adr7 ∧ adr1 = adr6 ∧ adr2 = adr0 ∧ adr3 = adr ∧ err1 = err), jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_journal_add5# (ND1, ND2, ND3, ND4, ND5, RI, FI, RO, FO ; ADR1, ADR2, ADR3, ADR4, ADR5, FS, LOG ; CSYNCED, ERR ) {if ri-cons(RI, FS) ∧ node-cons(ND1.key, ND1) ∧ node-cons(ND2.key, ND2) ∧ node-cons(ND3.key, ND3) ∧ node-cons(ND4.key, ND4) ∧ node-cons(ND5.key, ND5) then { choose adr1, adr2, adr3, adr4, adr5 with new(adr1 ' + adr2 ' + adr3 ' + (adr4 ' + adr5), FS) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ' + adr5 ') in {ADR1 := adr1, ADR2 := adr2, ADR3 := adr3, ADR4 := adr4, ADR5 := adr5; FS := FS[ADR1, ND1][ADR2, ND2][ADR3, ND3][ADR4, ND4] [ADR5, ND5 ], LOG := ((((LOG + ADR1) + ADR2) + ADR3) + ADR4) + ADR5, ERR := ESUCCESS} ifnone ERR := ENOSPC or {fail#(; ; ERR); ADR1 := ?, ADR2 := ?, ADR3 := ?, ADR4 := ?, ADR5 := ?}; CSYNCED := ?} else abort };