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Proof step 36 from proof refine-remove (previous step)

gstore2[m] = groupblock(gndx, lax, n0 + m1), ri[key] = @(m, m0, m1), remove-refsize0(gstore1) = gstore1, ri0 = ri, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range ri), refsize-cons(gstore1, range fi1), ri-inj(fi1), ri-inj(ri -- key), ri-inj(ri), key ∈ ri, m ∈ gstore2, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟨aubifs_core_index_remove#(key, fi1, jro1.keys, p_os.keys, nodes(gstore2 ↓, jro0), abs-log(nx, gstore2 ↓), jvalid2; ri)⟩ ( ri0 -- key = ri ∧ abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, (gstore2[m].ref-size:= n0)↓]) ∧ nodes(gstore2 ↓, jro0) = nodes(gstore2 ↓[m, (gstore2[m].ref-size:= n0)↓], jro0) ∧ (jvalid2 → jvalid0))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 37:
jvalid ↔ jvalid2, ri[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), fi = fi1, fo = p_os.keys, fs = nodes(gstore2 ↓, jro0), log = abs-log(nx, gstore2 ↓), remove-refsize0(gstore1) = gstore1, ri0 = ri, ro = jro1.keys, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, p_os.keys.inodes?, jro1.keys.inodes?, fi1.inos < pmaxino, ri.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore2[m, groupblock(gndx, lax, n0)] \ jro0), inv(gstore1), inv(gstore2 \ jro0), log-cons(abs-log(nx, gstore2 ↓), nodes(gstore2 ↓, jro0)), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range ri), ri-inj(ri), ri-inj(ri -- key), ri-inj(fi1), m ∈ gstore2, key ∈ ri, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 → jvalid0 ⊦ ⟨ri := ri -- key⟩ ( ri0 -- key = ri ∧ abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, (gstore2[m].ref-size:= n0)↓]) ∧ nodes(gstore2 ↓, jro0) = nodes(gstore2 ↓[m, (gstore2[m].ref-size:= n0)↓], jro0) ∧ (jvalid2 → jvalid0)), jmaxino = 0, pmaxino = 0, dups(nx)

Rule argument

pos: right 1

Additional information

Used simplifier rules: aubifs_core_index_remove#(KEY, FI, RO, FO, FS, LOG, CSYNCED; RI) {RI := RI -- KEY};