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Proof step 43 from proof inv-store (previous step)

gstore3[m3] = groupblock(gndx, lax, m6), fi2[key] = @(m3, m4, m5), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), m6 = n1 + m5, remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore3[m3, groupblock(gndx, lax, n1)] \ jro0), inv(gstore2), inv(gstore3 \ jro0), key-cons(key, nd), refsize-cons(gstore2, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi1), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi2), m3 ∈ gstore3, @(m0, m1, m2) ∈ gstore3, key ∈ fi2, m5 ≤ m6, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ ⟪index_get_gblock_refsize# (m0, fi2[key, @(m0, m1, m2)], fi1, jro0, gstore3[m3, gstore3[m3].ref-size:= n1], gstore2, nx, pmaxino, p_os, jvalid0; ; n0); gstore := gstore3[m3, gstore3[m3].ref-size:= n1]; index_set_gblock_refsize#(m0, n0 + m2, fi2[key, @(m0, m1, m2)], fi1, jro0, gstore2, nx, pmaxino, p_os, jvalid0; gstore); jmaxino := max(key.ino + 1, jmaxino)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi2[key, @(m0, m1, m2)].lebs ⊆ dom gstore ∧ refsize-cons(gstore, (range fi2 -- fi2[key]) ++ @(m0, m1, m2)) ∧ inv(gstore \ jro0) ∧ dom gstore2 ∪ elems nx = dom gstore ∪ jro0 ∧ gstore =○refsize gstore3), jmaxino = 0, pmaxino = 0, dups(nx), @(m0, m1, m2) ∈ fi2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), fi2[key] = @(m3, m4, m5), gstore3[m3] = groupblock(gndx, lax, n1 + m5), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, jmaxino ≠ 0, pmaxino ≠ 0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore3 \ jro0), inv(gstore2), inv(gstore3[m3, groupblock(gndx, lax, n1)] \ jro0), key-cons(key, nd), refsize-cons(gstore3, range fi2), refsize-cons(gstore2, range fi1), ri-inj(fi2), ri-inj(fi2[key, @(m0, m1, m2)]), ri-inj(fi1), key ∈ fi2, @(m0, m1, m2) ∈ gstore3, m3 ∈ gstore3, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2, ¬ dups(nx), ¬ @(m0, m1, m2) ∈ fi2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ ⟪index_get_gblock_refsize# (m0, fi2[key, @(m0, m1, m2)], fi1, jro0, gstore3[m3, gstore3[m3].ref-size:= n1], gstore2, nx, pmaxino, p_os, jvalid0; ; n0); gstore := gstore3[m3, gstore3[m3].ref-size:= n1]; index_set_gblock_refsize#(m0, n0 + m2, fi2[key, @(m0, m1, m2)], fi1, jro0, gstore2, nx, pmaxino, p_os, jvalid0; gstore); jmaxino := max(key.ino + 1, jmaxino)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi2[key, @(m0, m1, m2)].lebs ⊆ dom gstore ∧ refsize-cons(gstore, (range fi2 -- fi2[key]) ++ @(m0, m1, m2)) ∧ inv(gstore \ jro0) ∧ dom gstore2 ∪ elems nx = dom gstore ∪ jro0 ∧ gstore =○refsize gstore3)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)