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Proof step 6 from proof refine-remove (previous step)

fi = ri, remove-refsize0(gstore0) = gstore0, elems nx ∩ jro0 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, 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, ¬ dups(nx), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), jvalid2 → jvalid0 ⊦ ⟪index_index_remove#(key, fi1, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid0; adr, jvalid, fi); log := abs-log(nx, gstore ↓); fs := nodes(gstore ↓, jro0); if jvalid then let n = ? in {index_get_gblock_refsize#(adr.lnum, fi, fi1, jro0, gstore, gstore0, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi, fi1, jro0, gstore0, nx, pmaxino, p_os, jvalid0; gstore)}⟫ ⟨aubifs_core_index_remove#(key, fi1, jro1.keys, p_os.keys, fs, log, jvalid2; ri)⟩ (fi = ri ∧ log = abs-log(nx, gstore ↓) ∧ fs = nodes(gstore ↓, jro0) ∧ (jvalid2 → jvalid0))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 7:
fi = ri, fi0 = fi1, gstore = gstore1, gstore0 = gstore2, jro = jro0, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-inj(ri), ri-inj(fi1), pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟪jvalid := key ∈ fi; if jvalid then {adr := fi[key]; fi := fi -- key} else adr := ?; log := abs-log(nx, gstore2 ↓); fs := nodes(gstore2 ↓, jro0); if jvalid then let n = ? in {index_get_gblock_refsize#(adr.lnum, fi, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os, jvalid0; ; n); index_set_gblock_refsize#(adr.lnum, n - adr.size, fi, fi1, jro0, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)}⟫ ⟨aubifs_core_index_remove#(key, fi1, jro1.keys, p_os.keys, fs, log, jvalid2; ri)⟩ (fi = ri ∧ log = abs-log(nx, gstore2 ↓) ∧ fs = nodes(gstore2 ↓, jro0) ∧ (jvalid2 → jvalid0)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: index_index_remove# (KEY, PFI, PINVAL, PSTORE, PSTORE0, PNL, PMAXINO, P_OS, ISYNCED ; OLDADR, EXISTS, PRI ) {EXISTS := KEY ∈ PRI; if EXISTS then {OLDADR := PRI[KEY]; PRI := PRI -- KEY} else OLDADR := ? };