| abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr10, adr0 = adr4, adr1 = adr8, adr2 = adr7, adr3 = adr4, adr5 = adr8, adr6 = adr7, adr9 = adr10, fi = fi1, fo = p_os.keys, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nd = nd3, nd0 = nd4, nd1 = nd5, nd2 = nd6, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0), remove-refsize0(gstore0) = gstore0, ro = jro1.keys, 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, 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(nd3.key, nd3), node-cons(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd6.key, nd6), 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⌋ , jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ⟨if ri-cons(ri, fs) ∧ 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 with new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ') in {adr6 := adr1, adr5 := adr2, adr0 := adr3, adr := adr4; fs := fs[adr6, nd2][adr5, nd1][adr0, nd0][adr, nd], log := (((log + adr6) + adr5) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC or {fail#(; ; err); adr6 := ?, adr5 := ?, adr0 := ?, adr := ?}; jvalid := ?} else abort⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr2 = adr6 ∧ adr1 = adr5 ∧ adr3 = adr0 ∧ adr9 = adr ∧ err1 = err), jmaxino1 = 0, pmaxino = 0, dups(nx), dups(nx0) |
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓), adr = adr10, adr0 = adr4, adr1 = adr8, adr2 = adr7, adr3 = adr4, adr5 = adr8, adr6 = adr7, adr9 = adr10, fi = fi1, fo = p_os.keys, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), nd = nd3, nd0 = nd4, nd1 = nd5, nd2 = nd6, 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(nd6.key, nd6), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), node-cons(nd3.key, nd3), 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) ⊦ ⟨ choose adr1, adr2, adr3, adr4 with new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ' + adr4 ') in {adr6 := adr1, adr5 := adr2, adr0 := adr3, adr := adr4; fs := fs[adr6, nd2][adr5, nd1][adr0, nd0][adr, nd], log := (((log + adr6) + adr5) + adr0) + adr, err := ESUCCESS} ifnone err := ENOSPC or {fail#(; ; err); adr6 := ?, adr5 := ?, adr0 := ?, adr := ?}; jvalid := ?⟩ ( log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid1) ∧ adr2 = adr6 ∧ adr1 = adr5 ∧ adr3 = adr0 ∧ adr9 = adr ∧ err1 = err), jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx)