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Proof step 18 from proof refine-check-commit (previous step)

jro1.keys = jro1.keys, p_os.keys = fo, jvalid3 ↔ jvalid2, jvalid4 ↔ jvalid1, fi = fi1, fi2 = ri, fi3 = fi1, fo0 = fo, fs = nodes(gstore2 ↓, jro2), fs0 = fs, jmaxino0 = jmaxino, jro3 = jro1, log = abs-log(nx, gstore2 ↓), log0 = log, remove-refsize0(gstore1) = gstore1, ri = ri, ri0 = ri, ro0 = jro1.keys, dom remove-refsize0(gstore2) ∩ jro2 = ∅, elems nx ∩ jro2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro2, p_os.keys.inodes?, jro1.keys.inodes?, fo.inodes?, fi1.inos < pmaxino, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi.inos < pmaxino, inv(gstore2 \ jro2), inv(gstore1), inv-journal(nx, gstore2, gstore1, jro2), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro2)), log-cons(log, fs), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi), ri-cons(ri, nodes(gstore2 ↓, jro2)), ri-cons(ri, fs), ri-inj(fi1), ri-inj(ri), ri-inj(fi), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, fi.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro2) ⊦ [gjournal_commit#(jmaxino, jro1, ri; fi, jro2, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; err)] ( ⟨aubifs_core_commit#(ri0, ro0; fs0, fi3, fo0, log0; jvalid, err0)⟩ ( ( jro3.keys = ro0 ∧ p_os.keys = fo0 ∧ fi2 = ri0 ∧ fi = fi3 ∧ log0 = abs-log(nx, gstore2 ↓) ∧ fs0 = nodes(gstore2 ↓, jro2) ∧ (jvalid → jvalid0)) ∧ err = err0) → ⟨aubifs_core_check_commit#(ri, jro1.keys; fi1, fo, fs, log, jvalid2; err0)⟩ (p_os.keys = fo ∧ fi = fi1 ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro2) ∧ (jvalid2 → jvalid0) ∧ err = err0)), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
p_os.keys = fo, fi = fi1, fs = nodes(gstore2 ↓, jro2), log = abs-log(nx, gstore2 ↓), remove-refsize0(gstore1) = gstore1, elems nx ∩ jro2 = ∅, dom remove-refsize0(gstore2) ∩ jro2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro2, jmaxino ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, fi1.inos < pmaxino, inv(gstore1), inv(gstore2 \ jro2), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro2)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-cons(ri, nodes(gstore2 ↓, jro2)), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro2), jvalid2 → jvalid0 ⊦ [gjournal_commit#(jmaxino, jro1, ri; fi, jro2, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; err)] ( ⟨aubifs_core_commit#(ri, jro1.keys; fs, fi1, fo, log; jvalid, err0)⟩ (p_os.keys = fo ∧ fi = fi1 ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro2) ∧ (jvalid → jvalid0) ∧ err = err0) → ⟨aubifs_core_check_commit#(ri, jro1.keys; fi1, fo, fs, log, jvalid2; err0)⟩ (p_os.keys = fo ∧ fi = fi1 ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro2) ∧ (jvalid2 → jvalid0) ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)