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Proof step 67 from proof inv-store (previous step)

gstore3[m3] = groupblock(gndx, lax, n1 + m5), fi2[key] = @(m3, m4, m5), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), gstore3[m3, groupblock(gndx, lax, n1)][m0] = groupblock(gndx0, lax0, m6), 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), inv(gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)] \ 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), n ∈ gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)], m0 ∈ gstore3[m3, groupblock(gndx, lax, n1)], @(m0, m1, m2) ∈ gstore3, key ∈ fi2, m3 ∈ gstore3, m0 ∈ dom gstore3 ∪ jro0, pmaxino ≤ jmaxino, pmaxino ≤ max(key.ino + 1, jmaxino), fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ #(dom gstore3 ∪ jro0) = 0, gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)][n].ref-size = (((range fi2 -- @(m3, m4, m5)) ++ @(m0, m1, m2)) | n).size, jmaxino = 0, max(key.ino + 1, jmaxino) = 0, pmaxino = 0, dom gstore3 ∪ jro0 = ∅, dups(nx), @(m0, m1, m2) ∈ fi2

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 68:
gstore3[m3, groupblock(gndx, lax, n1)][m0] = groupblock(gndx0, lax0, m6), gstore3[@(m0, m1, m2)] = mkgnode(nd, m, boolvar, boolvar0), fi2[key] = @(m3, m4, m5), gstore3[m3] = groupblock(gndx, lax, n1 + m5), gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)][n] = groupblock(gndx1, lax1, m7), remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)] \ jro0), 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), m0 ∈ dom gstore3 ∪ jro0, m3 ∈ gstore3, key ∈ fi2, @(m0, m1, m2) ∈ gstore3, m0 ∈ gstore3[m3, groupblock(gndx, lax, n1)], n ∈ gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)], pmaxino ≤ max(key.ino + 1, jmaxino), pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore3, fi1.lebs ⊆ dom gstore2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ #(dom gstore3 ∪ jro0) = 0, jmaxino = 0, m7 = (((range fi2 -- @(m3, m4, m5)) ++ @(m0, m1, m2)) | n).size, max(key.ino + 1, jmaxino) = 0, pmaxino = 0, dom gstore3 ∪ jro0 = ∅, dups(nx), @(m0, m1, m2) ∈ fi2

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] → [gstore3[m3, groupblock(gndx, lax, n1)] [m0, groupblock(gndx0, lax0, m6 + m2) ] [n ], gndx1, lax1, m7]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore3[m3, groupblock(gndx, lax, n1)] [m0, groupblock(gndx0, lax0, m6 + m2) ] [n ], gndx1, lax1, m7