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Proof step 33 from proof refine-remove (previous step)

jvalid ↔ jvalid0, gstore2[m] = groupblock(gndx, lax, m2), ri[key] = @(m, m0, m1), fi = fi1, fi0 = ri -- key, gstore = gstore2, gstore0 = gstore1, gstore3 = gstore2, jro = jro0, lnum = m, n = m2 - m1, remove-refsize0(gstore1) = gstore1, ri0 = ri, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx = dom gstore[lnum, gstore[lnum].ref-size:= n] ∪ jro0, jro1.keys.inodes?, p_os.keys.inodes?, jro1 < jmaxino, p_os < pmaxino, ri.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore[lnum, gstore[lnum].ref-size:= n] \ 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), m ∈ gstore2, key ∈ ri, lnum ∈ gstore, pmaxino ≤ jmaxino, m2 ≥ m1, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟨aubifs_core_index_remove#(key, fi1, jro1.keys, p_os.keys, nodes(gstore3 ↓, jro0), abs-log(nx, gstore3 ↓), jvalid2; ri)⟩ ( ri0 -- key = ri ∧ abs-log(nx, gstore3 ↓) = abs-log(nx, gstore[lnum, gstore[lnum].ref-size:= n] ↓) ∧ nodes(gstore3 ↓, jro0) = nodes(gstore[lnum, gstore[lnum].ref-size:= n] ↓, jro0) ∧ (jvalid2 → jvalid0)), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
gstore2[m] = groupblock(gndx, lax, m2), 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, m2 - m1)] \ 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, m1 ≤ m2, 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:= (m2 - m1))↓]) ∧ nodes(gstore2 ↓, jro0) = nodes(gstore2 ↓[m, (gstore2[m].ref-size:= (m2 - m1))↓], jro0) ∧ (jvalid2 → jvalid0))

Rule argument

Additional information

Used simplifier rules: ⊦ groupblock(gndx, lax, m).ref-size:= m0 = groupblock(gndx, lax, m0); (s)% ⊦ gstore[m, gblock] ↓ = gstore ↓[m, gblock ↓]; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ n ∈ gstore → dom gstore ++ n = dom gstore; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)