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Proof step 153 from proof inv-gc-copy (previous step)

# ax = # ndx1, abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, ax0 = [], fi = fi2[ndx1.keys, ax], fi0 = fi2[ndx1.keys, ax], fi3 = fi1, gstore = gstore1, gstore0 = gstore3, jmaxino = 0, ndx = [], ndx2 = ndx4, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx1], nx = [], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, jro2 < jmaxino3, p_os < pmaxino, fi2.inos < jmaxino3, fi1.inos < pmaxino, fi2[ndx1.keys, ax].inos < jmaxino0, inv(gstore2 \ jro0), inv(gstore1), inv(gstore3 \ jro), key-cons(ndx1), key-cons(ndx4), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2[ndx1.keys, ax]), ri-inj(fi2), ri-inj(fi1), ri-inj(fi2[ndx1.keys, ax]), jmaxino3 ≤ jmaxino0, pmaxino ≤ jmaxino3, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ndx1.keys.toSet ⊆ dom fi2, ndx4.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi2[ndx1.keys, ax].lebs ⊆ dom gstore3, range fi2[ndx1.keys, ax] ⊆ dom nodes(gstore3 ↓, jro), dom gstore2 ⊆ dom gstore3, fi2.lebs ⊆ dom gstore3, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore3, jro) ⊦ ⟪index_get_leb_size(fi, fi1, jro, gstore3, gstore1, nx, pmaxino, p_os, jvalid0; ; n); ndx0 := ndx2; gjournal_split_nodes#(n - jmaxino; ndx2, ndx); if ndx = [] then err := EINVAL else {gjournal_journal_addn#(ndx, jvalid2, fi, fi1, gstore1, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore3, nx, jvalid0; err); if err = ESUCCESS then gjournal_gc_update_index#(jvalid1, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; ax0, ndx, jmaxino0, fi, gstore3)}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx3. ndx1 + ndx0 = ndx3 + ndx2) ∧ 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) ∧ ndx2.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore3 ↓, jro) ∧ dom gstore2 ⊆ dom gstore3 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅ ∧ (∃ ax, ndx3, ndx4. ndx1 + ndx0 = ndx3 + ndx4 ∧ (err = ESUCCESS → ndx4 = ndx2) ∧ new(ax, nodes(gstore2 ↓, jro0)) ∧ ¬ dups(ax) ∧ # ax = # ndx3 ∧ fi = fi2[ndx3.keys, ax] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx3] ∧ abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax) ∧ (err = ESUCCESS ⊃ # ndx2;0) < # ndx4), jmaxino3 = 0, ndx4 = [], pmaxino = 0, dups(ndx4.keys), dups(ndx1.keys), dups(ndx1.keys + ndx4.keys), dups(nx1), dups(nx), dups(ax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 154:
abs-log(nx1, gstore2 ↓) = [], dom gstore1 = dom gstore3 ∪ jro, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0), remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jmaxino3 ≠ 0, ndx4 ≠ [], pmaxino ≠ 0, fi1.inos < pmaxino, fi2.inos < jmaxino3, p_os < pmaxino, jro2 < jmaxino3, fi2.inos < jmaxino0, inv(gstore3 \ jro), inv(gstore1), inv(gstore2 \ jro0), key-cons(ndx4), refsize-cons(gstore3, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), pmaxino ≤ jmaxino0, pmaxino ≤ jmaxino3, jmaxino3 ≤ jmaxino0, dom gstore2 ⊆ dom gstore3, fi2.lebs ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), ndx4.keys.toSet ⊆ dom fi2, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, ¬ dups(nx1), ¬ dups(ndx4.keys), jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0) ⊦ ⟪index_get_leb_size(fi2, fi1, jro, gstore3, gstore1, [], pmaxino, p_os, jvalid0; ; n); ndx0 := ndx4; ndx3 := ndx4; ndx := []; gjournal_split_nodes#(n - 0; ndx4, ndx); nx := []; fi := fi2; if ndx = [] then err := EINVAL else {ax0 := []; gjournal_journal_addn#(ndx, jvalid2, fi, fi1, gstore1, pmaxino, p_os; ax0, jvalid1, jmaxino1, jro, gstore3, nx, jvalid0; err); if err = ESUCCESS then gjournal_gc_update_index#(jvalid1, fi1, jro, gstore1, nx, pmaxino, p_os, jvalid0; ax0, ndx, jmaxino0, fi, gstore3)}⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (∃ ndx. ndx0 = ndx + ndx4) ∧ 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) ∧ ndx4.keys.toSet ⊆ dom fi ∧ range fi ⊆ dom nodes(gstore3 ↓, jro) ∧ dom gstore2 ⊆ dom gstore3 ∧ (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅ ∧ (∃ ndx, ndx1. ndx0 = ndx + ndx1 ∧ (err = ESUCCESS → ndx1 = ndx4) ∧ new(abs-log(nx, gstore3 ↓), nodes(gstore2 ↓, jro0)) ∧ ¬ dups(abs-log(nx, gstore3 ↓)) ∧ # abs-log(nx, gstore3 ↓) = # ndx ∧ fi = fi2[ndx.keys, abs-log(nx, gstore3 ↓)] ∧ nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[abs-log(nx, gstore3 ↓), ndx]) ∧ (err = ESUCCESS ⊃ # ndx4;0) < # ndx3)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ [] + ndx = ndx; (s)% ⊦ ¬ dups([]); (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ [] + kx = kx; (s)% ⊦ key-cons([]); (s)% ⊦ ∅ ⊆ ks; (s)% ⊦ [].toSet = ∅; (s)% ⊦ fs[[], []] = fs; (s)% ⊦ [] + ax = ax; (s)% ⊦ ri[[], []] = ri; (s)% ⊦ [].keys = []; (s)% ⊦ ¬ dups([]); (s)% ⊦ new([], fs); (s)% ⊦ # ndx = 0 ↔ ndx = []; (s)% ⊦ # [] = 0; (s)%sub-trans: ⊦ ns ⊆ ns0 ∧ ns0 ⊆ ns1 → ns ⊆ ns1; (forward) from specification set-basic[nat-set]% ⊦ ¬ dups([]); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + ax0 = [] ↔ ax = [] ∧ ax0 = []; (as)% ⊦ abs-log([], gstore) = []; (s)% ⊦ ∅ \ ns = ∅; (s)% ⊦ [].toSet = ∅; (s)%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ns ∩ ∅ = ∅; (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 ∪ ∅ = ns; (s)% ⊦ elems [] = ∅; (s)