| 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) ⊦ ⟨fail#(; ; err); adr8 := ?, adr7 := ?, adr6 := ?, adr0 := ?, adr := ?; jvalid := ?⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr13 = adr8 ∧ adr12 = adr7 ∧ adr1 = adr6 ∧ adr2 = adr0 ∧ adr3 = adr ∧ err1 = err), ⟨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; jvalid := ?⟩ ( 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) |
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr5, adr0 = adr11, 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, ⌊err1⌋ , ¬ dups(nx), ¬ dups(nx0), jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ⟨choose adr1, adr2, adr3, adr7, adr5 with new(adr1 ' + adr2 ' + adr3 ' + (adr7 ' + adr5), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr7 ' + adr5 ') in {adr9 := adr1, adr10 := adr2, adr4 := adr3, adr0 := adr7, adr := adr5; fs := fs[adr9, nd7][adr10, nd6][adr4, nd1][adr0, nd5][adr, nd4], log := ((((log + adr9) + adr10) + adr4) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC; jvalid := ?⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr13 = adr9 ∧ adr12 = adr10 ∧ adr1 = adr4 ∧ adr11 = adr0 ∧ adr5 = adr ∧ err1 = err), ⟨fail#(; ; err); adr2 := ?, adr3 := ?, adr6 := ?, adr0 := ?, adr := ?; jvalid := ?⟩ ((jvalid → jvalid1) ∧ adr9 = adr2 ∧ adr10 = adr3 ∧ adr4 = adr6 ∧ adr11 = adr0 ∧ adr5 = adr ∧ err1 = err)