[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 38 from proof refine-add4 (previous step)

1 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr7 ' + adr1 ' + adr9 ' + ax0, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr7, nd6][adr1, nd5][adr9, nd4][ax0, nd3 '], remove-refsize0(gstore0) = gstore0, 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, adr1 ≠ adr9, adr7 ≠ adr1, adr7 ≠ adr9, jmaxino1 ≠ 0, pmaxino ≠ 0, 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(ax0, nodes(gstore ↓, jro0)), node-cons(nd6.key, nd6), node-cons(nd5.key, nd5), node-cons(nd4.key, nd4), node-cons(nd3.key, nd3), nodes-cons(adr7 ' + adr1 ' + adr9 ' + ax0, nd6 ' + nd5 ' + nd4 ' + nd3 ', 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, ¬ dups(nx), ¬ dups(nx0), ¬ dups(ax0), ¬ adr9 ∈ nodes(gstore ↓, jro0), ¬ adr1 ∈ ax0, ¬ adr7 ∈ ax0, ¬ adr7 ∈ nodes(gstore ↓, jro0), ¬ adr1 ∈ nodes(gstore ↓, jro0), ¬ adr9 ∈ ax0, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ∃ adr2, adr3, adr4, adr8. ¬ adr2 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr3 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr4 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr8 ∈ nodes(gstore ↓, jro0) ∧ adr2 ≠ adr3 ∧ adr2 ≠ adr4 ∧ adr2 ≠ adr8 ∧ adr3 ≠ adr4 ∧ adr3 ≠ adr8 ∧ adr4 ≠ adr8 ∧ ⟨adr6 := adr2, adr5 := adr3, adr0 := adr4, adr := adr8; fs := nodes(gstore ↓, jro0)[adr6, nd6][adr5, nd5][adr0, nd4][adr, nd3], log := (((abs-log(nx, gstore ↓) + adr6 ') + adr5 ') + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ ( log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr7 = adr6 ∧ adr1 = adr5 ∧ adr9 = adr0 ∧ ax0[0] = adr ∧ ESUCCESS = err)

User applied rule constructor cut

And obtained the following new goals

Proof step 39:
1 = # ax0, abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr7 ' + adr1 ' + adr9 ' + ax0, ax0 = adr10 + ax1, nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr7, nd6][adr1, nd5][adr9, nd4][ax0, nd3 '], 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, 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(ax0, nodes(gstore ↓, jro0)), node-cons(nd3.key, nd3), node-cons(nd4.key, nd4), node-cons(nd5.key, nd5), node-cons(nd6.key, nd6), nodes-cons(adr7 ' + adr1 ' + adr9 ' + ax0, nd6 ' + nd5 ' + nd4 ' + nd3 ', 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, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid5 → jvalid4, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro) ⊦ ∃ adr2, adr3, adr4, adr8. ¬ adr2 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr3 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr4 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr8 ∈ nodes(gstore ↓, jro0) ∧ adr2 ≠ adr3 ∧ adr2 ≠ adr4 ∧ adr2 ≠ adr8 ∧ adr3 ≠ adr4 ∧ adr3 ≠ adr8 ∧ adr4 ≠ adr8 ∧ ⟨adr6 := adr2, adr5 := adr3, adr0 := adr4, adr := adr8; fs := nodes(gstore ↓, jro0)[adr6, nd6][adr5, nd5][adr0, nd4][adr, nd3], log := (((abs-log(nx, gstore ↓) + adr6 ') + adr5 ') + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ ( log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr7 = adr6 ∧ adr1 = adr5 ∧ adr9 = adr0 ∧ ax0[0] = adr ∧ ESUCCESS = err), adr1 = adr9, adr7 = adr1, adr7 = adr9, jmaxino1 = 0, pmaxino = 0, dups(nx), dups(nx0), dups(ax0), adr9 ∈ nodes(gstore ↓, jro0), adr1 ∈ ax0, adr7 ∈ ax0, adr7 ∈ nodes(gstore ↓, jro0), adr1 ∈ nodes(gstore ↓, jro0), adr9 ∈ ax0

Rule argument

var: ax0

Additional information

Used simplifier rules: address-list freely generated by [], +;;% ⊦ ax + [] = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ # [] = 0; (s)