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Proof step 58 from proof inv-truncate (previous step)

gstore2[m] = groupblock(gndx, lax, n1 + m1), gstore2[m, groupblock(gndx, lax, n1)][n] = groupblock(gndx0, lax0, m2), gstore2[n] = groupblock(gndx1, lax1, m3), dom gstore2 = dom gstore3, remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, p_os < pmaxino, fi1.inos < jmaxino, fi2.inos < pmaxino, gstore2 =○refsize gstore3, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro), inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), refsize-cons(gstore3, range fi1), refsize-cons(gstore1, range fi2), ri-inj(fi1), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi2), @(m, m0, m1) ∈ as0, m ∈ gstore2, n ∈ gstore2[m, groupblock(gndx, lax, n1)], pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, as0.lebs ⊆ dom gstore3, n ∈ gstore2 → m3 = ((range(fi1 \ datakeys(key, n0, fi1)) | n) ∪ (as0 | n)).size, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro) ⊦ # as0 = 0, as0 = ∅, m2 = ((range(fi1 \ datakeys(key, n0, fi1)) | n) ∪ ((as0 -- @(m, m0, m1)) | n)).size, pmaxino = 0, dups(nx)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 59:
gstore2[n] = groupblock(gndx1, lax1, m3), gstore2[m, groupblock(gndx, lax, n1)][n] = groupblock(gndx0, lax0, m2), gstore2[m] = groupblock(gndx, lax, n1 + m1), dom gstore2 = dom gstore3, n = m, remove-refsize0(gstore1) = gstore1, as0 ∩ range(fi1 \ datakeys(key, n0, fi1)) = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2.inos < pmaxino, fi1.inos < jmaxino, p_os < pmaxino, gstore2 =○refsize gstore3, inv(gstore2[m, groupblock(gndx, lax, n1)] \ jro), inv(gstore2 \ jro), inv(gstore1), inv(gstore3 \ jro), refsize-cons(gstore1, range fi2), refsize-cons(gstore3, range fi1), ri-inj(fi2), ri-inj(fi1 \ datakeys(key, n0, fi1)), ri-inj(fi1), n ∈ gstore2[m, groupblock(gndx, lax, n1)], m ∈ gstore2, @(m, m0, m1) ∈ as0, pmaxino ≤ jmaxino, as0.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore1, fi1.lebs ⊆ dom gstore3, jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro), jvalid2 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro), n ∈ gstore2 → m3 = ((range(fi1 \ datakeys(key, n0, fi1)) | n) ∪ (as0 | n)).size ⊦ # as0 = 0, as0 = ∅, m2 = ((range(fi1 \ datakeys(key, n0, fi1)) | n) ∪ ((as0 -- @(m, m0, m1)) | n)).size, pmaxino = 0, dups(nx)

Rule argument

fma: n = m

Additional information

Used simplifier rules: ⊦ n ≠ n0 → gstore[n0, gblock][n] = gstore[n]; (s)% ⊦ m ≠ n → (as -- @(m, m0, m1)) | n = as | n; (s)% ⊦ n ≠ n0 → (n ∈ gstore[n0, gblock] ↔ n ∈ gstore); (s)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws) Used formulas: n = m