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

jvalid ↔ jvalid0, 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), fi = fi1, fi0 = fi2[key, @(m0, m1, m2)], gstore = gstore3[m3, groupblock(gndx, lax, n1)], gstore0 = gstore2, jro = jro0, lnum = m0, n = m6 + m2, remove-refsize0(gstore2) = gstore2, elems nx ∩ jro0 = ∅, dom gstore2 ∪ elems nx = dom gstore3 ∪ jro0, dom gstore2 ∪ elems nx = dom gstore[lnum, gstore[lnum].ref-size:= n] ∪ 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(gstore[lnum, gstore[lnum].ref-size:= n] \ 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), m0 ∈ gstore3[m3, groupblock(gndx, lax, n1)], @(m0, m1, m2) ∈ gstore3, key ∈ fi2, m3 ∈ gstore3, lnum ∈ gstore, pmaxino ≤ jmaxino, fi1.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro0) ⊦ jmaxino = 0, pmaxino = 0, dups(nx), @(m0, m1, m2) ∈ fi2, jro1 < max(key.ino + 1, jmaxino) ∧ pmaxino ≤ max(key.ino + 1, jmaxino) ∧ fi2.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < max(key.ino + 1, jmaxino) ∧ max(key.ino + 1, jmaxino) ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore[lnum, gstore[lnum].ref-size:= n], jro0)) ∧ fi2[key, @(m0, m1, m2)].lebs ⊆ dom gstore[lnum, gstore[lnum].ref-size:= n] ∧ refsize-cons(gstore[lnum, gstore[lnum].ref-size:= n], (range fi2 -- fi2[key]) ++ @(m0, m1, m2)) ∧ gstore[lnum, gstore[lnum].ref-size:= n] =○refsize gstore3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
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), 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)], 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, max(key.ino + 1, jmaxino) = 0, pmaxino = 0, dom gstore3 ∪ jro0 = ∅, dups(nx), @(m0, m1, m2) ∈ fi2, gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)] =○refsize gstore3 ∧ refsize-cons(gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)], (range fi2 -- @(m3, m4, m5)) ++ @(m0, m1, m2)) ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3[m3, groupblock(gndx, lax, n1)][m0, groupblock(gndx0, lax0, m6 + m2)], jro0)) ∧ fi2.inos ∪ (key.inode? ⊃ ∅ ++ key.ino;∅) < max(key.ino + 1, jmaxino)

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]% ⊦ m + 1 ≠ 0; (s)% ⊦ max(n, m) = 0 ↔ n = 0 ∧ m = 0; (ws)% ⊦ ¬ max(n, m) < m; (s)%ne-01: ⊦ n ∈ ns → ns ≠ ∅; (forward) from specification set-basic[nat-set]%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ groupblock(gndx, lax, m).ref-size:= m0 = groupblock(gndx, lax, m0); (s)% ⊦ ns ++ n = ns ↔ n ∈ ns; (s)% ⊦ ri.lebs ⊆ dom gstore → ri[key, @(m, m1, m2)].lebs ⊆ dom gstore ++ m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ns < n → ns < max(m + 1, n); (s)%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]% ⊦ (ns ++ n) ∪ ns0 = (ns ∪ ns0) ++ n; (s)% ⊦ n ∈ gstore → dom gstore ++ n = dom gstore; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)