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Proof step 3 from proof refine-remove (previous step)

fi = ri, fs = nodes(gstore ↓, jro0), log = abs-log(nx, gstore ↓), remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro.keys.inodes?, p_os.keys.inodes?, jro < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore \ jro0), inv(gstore0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore, range ri), refsize-cons(gstore0, range fi1), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore0, ¬ dups(nx), jvalid → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0) ⊦ ⟪gjournal_index_remove#(key, fi1, jro0, gstore0, nx, pmaxino, p_os, jvalid0; fi, gstore)⟫ ⟨aubifs_core_index_remove#(key, fi1, jro.keys, p_os.keys, fs, log, jvalid; ri)⟩ (fi = ri ∧ log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid0))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
fi = ri, fi0 = fi1, fs = nodes(gstore ↓, jro0), jro = jro0, log = abs-log(nx, gstore ↓), remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore0), inv(gstore \ jro0), log-cons(abs-log(nx, gstore ↓), nodes(gstore ↓, jro0)), refsize-cons(gstore0, range fi1), refsize-cons(gstore, range ri), ri-inj(fi1), ri-inj(ri), pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore0, ri.lebs ⊆ dom gstore, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid → jvalid0 ⊦ ⟪let jvalid = ?, adr = ? in {index_index_remove#(key, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; adr, jvalid, fi); if jvalid then let n = ? in {index_get_gblock_refsize#(adr.lnum, fi, fi0, jro, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi, fi0, jro, gstore0, nx, pmaxino, p_os, jvalid0; gstore)}}⟫ ⟨aubifs_core_index_remove#(key, fi1, jro1.keys, p_os.keys, fs, log, jvalid; ri)⟩ (fi = ri ∧ log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid → jvalid0)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: gjournal_index_remove# (KEY, PFI, PINVAL, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED; PRI, PSTORE) {let EXISTS = ?, OLDADR = ? in {index_index_remove# (KEY, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; OLDADR, EXISTS, PRI); if EXISTS then let N = ? in {index_get_gblock_refsize# (OLDADR.lnum, PRI, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; ; N); index_set_gblock_refsize# (OLDADR.lnum, N - OLDADR.size, PRI, PFI, PINVAL, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; PSTORE)}} };