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Proof step 43 from proof refine-remove (previous step)

ri[key] = @(m, m0, m1), gstore2[m] = groupblock(gndx, lax, n0 + m1), 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(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 ⊦ abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]), jmaxino = 0, pmaxino = 0, dups(nx), (n ∈ gstore2 → n ∈ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]) ∧ ( n ∈ gstore2 → gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n].gndlist = gstore2[n] ↓.gndlist ∧ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n].ladrlist = gstore2[n] ↓.ladrlist)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
gstore2[m] = groupblock(gndx, lax, n0 + m1), ri[key] = @(m, m0, m1), gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)][n] = groupblock(gndx0, lax0, m2), 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) ⊦ abs-log(nx, gstore2 ↓) = abs-log(nx, gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]), jmaxino = 0, pmaxino = 0, dups(nx), (n ∈ gstore2 → n ∈ gstore2 ↓[m, groupblock(prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0)]) ∧ (n ∈ gstore2 → gndx0 = gstore2[n] ↓.gndlist ∧ lax0 = gstore2[n] ↓.ladrlist)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore2 ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0) ] [n ], gndx0, lax0, m2]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore2 ↓ [m, groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), n0) ] [n ], gndx0, lax0, m2