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Proof step 32 from proof refine-add2 (previous step)

abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr3 ' + adr1 ', nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr3, nd2][adr1, nd1], 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, adr3 ≠ adr1, 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)), node-cons(nd2.key, nd2), node-cons(nd1.key, nd1), nodes-cons(adr3 ' + adr1 ', nd2 ' + nd1 ', 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), adr1 ∈ abs-log(nx0, gstore1 ↓), pmaxino ≤ jmaxino1, ri.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, dom gstore ⊆ dom gstore1, ¬ dups(nx0), ¬ dups(nx), ¬ adr3 ∈ nodes(gstore ↓, jro0), ¬ adr1 ∈ nodes(gstore ↓, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore1, jro), jvalid5 → jvalid4, jvalid3 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ∃ adr2, adr4. ¬ adr2 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr4 ∈ nodes(gstore ↓, jro0) ∧ adr2 ≠ adr4 ∧ ⟨adr0 := adr2, adr := adr4; fs := nodes(gstore ↓, jro0)[adr0, nd2][adr, nd1], log := (abs-log(nx, gstore ↓) + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ adr1 = adr ∧ ESUCCESS = err)

User applied rule exists right

And obtained the following new goals

Proof step 33:
abs-log(nx0, gstore1 ↓) = abs-log(nx, gstore ↓) + adr3 ' + adr1 ', nodes(gstore1 ↓, jro) = nodes(gstore ↓, jro0)[adr3, nd2][adr1, nd1], 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)), node-cons(nd1.key, nd1), node-cons(nd2.key, nd2), nodes-cons(adr3 ' + adr1 ', nd2 ' + nd1 ', 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), adr1 ∈ abs-log(nx0, gstore1 ↓), 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) ⊦ ¬ adr3 ∈ nodes(gstore ↓, jro0) ∧ ¬ adr1 ∈ nodes(gstore ↓, jro0) ∧ adr3 ≠ adr1 ∧ ⟨adr0 := adr3, adr := adr1; fs := nodes(gstore ↓, jro0)[adr0, nd2][adr, nd1], log := (abs-log(nx, gstore ↓) + adr0 ') + adr ', err := ESUCCESS; jvalid := ?⟩ (log = abs-log(nx0, gstore1 ↓) ∧ fs = nodes(gstore1 ↓, jro) ∧ (jvalid → jvalid1) ∧ adr3 = adr0 ∧ adr1 = adr ∧ ESUCCESS = err), adr3 = adr1, jmaxino1 = 0, pmaxino = 0, dups(nx0), dups(nx), adr3 ∈ nodes(gstore ↓, jro0), adr1 ∈ nodes(gstore ↓, jro0)

Rule argument

pos: right 1 terms: adr3, adr1 abort: F discard: T computed: T

Additional information

Used terms: adr3, adr1