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Proof step 38 from proof refine-remove (previous step)

jvalid ↔ jvalid2, gstore2[m] = groupblock(gndx, lax, n0 + m1), ri[key] = @(m, m0, 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, 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, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ jmaxino = 0, pmaxino = 0, dups(nx), ri0 -- key = ri -- key ∧ 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
gstore2[m] = groupblock(gndx, lax, n0 + m1), ri[key] = @(m, m0, m1), 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), 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, jvalid2 → jvalid0, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ jmaxino = 0, pmaxino = 0, dups(nx), abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]) ∧ nodes(gstore2 ↓, jro0) = nodes(gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)], jro0)

Rule argument

Additional information

Used simplifier rules: ⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0); (s)% ⊦ groupblock(gndx, lax, m).ref-size:= m0 = groupblock(gndx, lax, m0); (s)