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Proof step 28 from proof refine-remove (previous step)

syn0 ↔ jvalid0, ri[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, m2), fi2 = ri -- key, fi3 = fi1, ginval1 = jro0, ginval2 = p_os, gstore = gstore2, gstore3 = gstore1, maxino1 = m, maxino2 = pmaxino, n0 = m2 - m1, nx0 = nx, remove-refsize0(gstore1) = gstore1, 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(gstore1), inv(gstore2 \ jro0), inv-journal(nx, gstore2, gstore1, 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), key ∈ ri, m ∈ gstore2, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore1, ri.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0), jvalid2 → jvalid0 ⊦ [index_set_gblock_refsize#(m, m2 - m1, ri -- key, fi1, jro0, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)] ( inv-journal(nx0, gstore2, gstore3, ginval1) → ⟨ri0 := ri; aubifs_core_index_remove#(key, fi1, jro1.keys, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid2; ri)⟩ (ri0 -- key = ri ∧ abs-log(nx, gstore ↓) = abs-log(nx, gstore2 ↓) ∧ nodes(gstore ↓, jro0) = nodes(gstore2 ↓, jro0) ∧ (jvalid2 → jvalid0))), jmaxino = 0, pmaxino = 0, dups(nx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
gstore2[m] = groupblock(gndx, lax, m2), ri[key] = @(m, m0, m1), gstore = gstore2, remove-refsize0(gstore1) = gstore1, 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), 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, pmaxino ≤ jmaxino, ri.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ [index_set_gblock_refsize#(m, m2 - m1, ri -- key, fi1, jro0, gstore1, nx, pmaxino, p_os, jvalid0; gstore2)] ( inv(gstore2 \ jro0) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 → ⟨ri0 := ri; aubifs_core_index_remove#(key, fi1, jro1.keys, p_os.keys, nodes(gstore ↓, jro0), abs-log(nx, gstore ↓), jvalid2; ri)⟩ (ri0 -- key = ri ∧ abs-log(nx, gstore ↓) = abs-log(nx, gstore2 ↓) ∧ nodes(gstore ↓, jro0) = nodes(gstore2 ↓, jro0) ∧ (jvalid2 → jvalid0)))

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)