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Proof step 44 from proof inv-gc-copy (previous step)

# ax = # ndx1, nd ' + ndx2 = ndx0 + ndx3, abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, fi = fi2[ndx1.keys, ax], ndx0 = [], nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx1], remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, n0 < nd.flashsize, fi2[ndx1.keys, ax].inos < jmaxino0, fi1.inos < pmaxino, fi2.inos < jmaxino3, p_os < pmaxino, jro2 < jmaxino3, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro0), inv(gstore3[nx.last]), key-cons(ndx1), key-cons(nd.key, nd), key-cons(ndx2), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, range fi2[ndx1.keys, ax]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi2[ndx1.keys, ax]), ri-inj(fi1), ri-inj(fi2), nd.key ∈ fi2, nx.last ∈ gstore3, ndx0.flashsize ≤ LEB_SIZE, n0 ≤ LEB_SIZE, pmaxino ≤ jmaxino0, pmaxino ≤ jmaxino3, jmaxino3 ≤ jmaxino0, dom gstore2 ⊆ dom gstore3, range fi2[ndx1.keys, ax] ⊆ dom nodes(gstore3 ↓, jro), fi2[ndx1.keys, ax].lebs ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), ndx2.keys.toSet ⊆ dom fi2, ndx1.keys.toSet ⊆ dom fi2, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid1 → valid-journal-head(nx, gstore3, jro), nd ∈ ndx0 ∨ nd ∈ ndx3, ndx3 = [] ∨ LEB_SIZE < ndx0.flashsize + ndx3.head.flashsize ⊦ jmaxino3 = 0, nx = [], pmaxino = 0, dups(ndx2.keys), dups(ndx1.keys), dups(ndx1.keys + ndx2.keys), dups(nx1), dups(nx), dups(ax), nd.key ∈ ndx2.keys, nd.key ∈ ndx1.keys, (EINVAL = ESUCCESS ∨ ⌊EINVAL⌋ ) ∧ (∃ ndx. ndx1 + nd ' + ndx2 = ndx + ndx3) ∧ jmaxino3 ≤ jmaxino0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro)) ∧ fi.inos < jmaxino0 ∧ fi.lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi) ∧ inv(gstore3 \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore3 ∪ jro ∧ ri-inj(fi) ∧ ndx3.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore3 ↓, jro) ∧ dom gstore2 ⊆ dom gstore3 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅ ∧ (∃ ax, ndx0, ndx. ndx1 + nd ' + ndx2 = ndx0 + ndx ∧ (EINVAL = ESUCCESS → ndx = ndx3) ∧ new(ax, nodes(gstore2 ↓, jro0)) ∧ ¬ dups(ax) ∧ # ax = # ndx0 ∧ fi = fi2[ndx0.keys, ax] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx0] ∧ abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax) ∧ ¬ # ndx2 < (EINVAL = ESUCCESS ⊃ # ndx3;0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
# ax = # ndx1, abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx1], remove-refsize0(gstore1) = gstore1, elems nx ∩ jro = ∅, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, fi2[ndx1.keys, ax].inos < jmaxino0, fi1.inos < pmaxino, fi2.inos < jmaxino3, p_os < pmaxino, jro2 < jmaxino3, LEB_SIZE < nd.flashsize, n0 < nd.flashsize, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro0), inv(gstore3[nx.last]), key-cons(ndx1), key-cons(nd.key, nd), key-cons(ndx2), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, range fi2[ndx1.keys, ax]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi2[ndx1.keys, ax]), ri-inj(fi1), ri-inj(fi2), nd.key ∈ fi2, nx.last ∈ gstore3, n0 ≤ LEB_SIZE, pmaxino ≤ jmaxino0, pmaxino ≤ jmaxino3, jmaxino3 ≤ jmaxino0, dom gstore2 ⊆ dom gstore3, range fi2[ndx1.keys, ax] ⊆ dom nodes(gstore3 ↓, jro), fi2[ndx1.keys, ax].lebs ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), ndx2.keys.toSet ⊆ dom fi2, ndx1.keys.toSet ⊆ dom fi2, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid1 → valid-journal-head(nx, gstore3, jro) ⊦ jmaxino3 = 0, nx = [], pmaxino = 0, dups(ndx2.keys), dups(ndx1.keys), dups(ndx1.keys + ndx2.keys), dups(nx1), dups(nx), dups(ax), nd.key ∈ ndx2.keys, nd.key ∈ ndx1.keys, ∃ ax0, ndx, ndx0. ndx1 + nd ' + ndx2 = ndx + ndx0 ∧ new(ax0, nodes(gstore2 ↓, jro0)) ∧ ¬ dups(ax0) ∧ # ax0 = # ndx ∧ fi2[ndx1.keys, ax] = fi2[ndx.keys, ax0] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, ndx] ∧ abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax0

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ key ∈ dom ri ↔ key ∈ ri; (s)% ⊦ ks ⊆ ks0 → (ks ++ key ⊆ ks0 ∪ ks1 ↔ key ∈ ks0 ∨ key ∈ ks1); (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]%unc: ⊦ ks ∪ ks0 = ks0 ∪ ks; from specification set-union[node-index]%una: ⊦ (ks ∪ ks0) ∪ ks1 = ks ∪ ks0 ∪ ks1; from specification set-union[node-index]% ⊦ ks ∪ ∅ = ks; (s)% ⊦ (ks ++ key) ∪ ks0 = (ks ∪ ks0) ++ key; (s)% ⊦ key '.toSet = ∅ ++ key; (s)% ⊦ (kx + kx0).toSet = kx.toSet ∪ kx0.toSet; (s)% ⊦ key + kx = key ' + kx; (s)% ⊦ (nd ' + ndx).keys = nd.key + ndx.keys; (s)% ⊦ ndx + ndx0 = ndx1 + ndx0 ↔ ndx = ndx1; (s)% ⊦ (nd ' + ndx).head = nd; (s)% ⊦ nd ' + ndx ≠ []; (s)% ⊦ nd ∈ nd0 ' + ndx ↔ nd = nd0 ∨ nd ∈ ndx; (s)%in-14: ⊦ nd ' + ndx = ndx0 → nd ∈ ndx0; (forward) from specification list[node-list]% ⊦ ¬ m < 0; (s)%# kx = # ax ⊦ dom ri[kx, ax] = dom ri ∪ kx.toSet; (s)% ⊦ # ndx.keys = # ndx; (s)% ⊦ ⌊EINVAL⌋ ; (s)% ⊦ ESUCCESS ≠ EINVAL; (s)% ⊦ ¬ nd ∈ []; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ 0 ≤ m; (s)% ⊦ [].flashsize = 0; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ [] + ndx = ndx; (s)