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Proof step 201 from proof inv-gc-copy (previous step)

jvalid6 ↔ jvalid3, jvalid5 ↔ jvalid, jvalid2 ↔ jvalid4, err1 = ESUCCESS, fi1 = fi2, gstore1 = gstore2, jmaxino2 = jmaxino, jmaxino4 = jmaxino, jro1 = jro0, jro3 = jro0, ndx3 = ndx, ndx5 = ndx, nx0 = nx1, remove-refsize0(gstore0) = gstore0, elems nx1 ∩ jro0 = ∅, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro0, jro2 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi0.inos < pmaxino, fi.inos < jmaxino0, inv(gstore2 \ jro0), inv(gstore0), inv-journal(nx, gstore, gstore0, jro), key-cons(ndx), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi), ri-inj(fi2), ri-inj(fi0), ri-inj(fi), pmaxino ≤ jmaxino, jmaxino0 ≥ jmaxino4, fi2.lebs ⊆ dom gstore2, fi0.lebs ⊆ dom gstore0, ndx.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi.lebs ⊆ dom gstore, ndx2.keys.toSet ⊆ dom fi, range fi ⊆ dom nodes(gstore ↓, jro), dom gstore2 ⊆ dom gstore, jvalid ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), ∃ ndx0. ndx5 = ndx0 + ndx2, ∃ ax, ndx0, ndx1. ndx5 = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = ndx2) ∧ new(ax, nodes(gstore2 ↓, jro3)) ∧ ¬ dups(ax) ∧ # ax = # ndx0 ∧ fi = fi2[ndx0.keys, ax] ∧ nodes(gstore ↓, jro) = nodes(gstore2 ↓, jro3)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx1, gstore2 ↓) + ax, err = ESUCCESS ∨ ⌊err⌋ ⊦ jmaxino = 0, pmaxino = 0, dups(nx1), dups(ndx.keys), jro2 < jmaxino0 ∧ pmaxino ≤ jmaxino0 ∧ fi.inos < jmaxino0 ∧ jmaxino0 ≠ 0 ∧ (jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv(gstore \ jro) ∧ elems nx ∩ jro = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ jro ∧ ri-inj(fi) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ jmaxino2 ≤ jmaxino0 ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ (∃ ax, ndx0, ndx1. ndx3 = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = []) ∧ new(ax, nodes(gstore1 ↓, jro1)) ∧ # ax = # ndx0 ∧ ¬ dups(ax) ∧ fi = fi1[ndx0.keys, ax] ∧ nodes(gstore ↓, jro) = nodes(gstore1 ↓, jro1)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax), err = ESUCCESS ∧ ndx2 ≠ []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 202:
# ax = # ndx4, ndx4 + ndx1 = ndx0 + ndx2, abs-log(nx, gstore ↓) = abs-log(nx1, gstore2 ↓) + ax, nodes(gstore ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx4], remove-refsize0(gstore0) = gstore0, elems nx ∩ jro = ∅, elems nx1 ∩ jro0 = ∅, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ jro, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro0, jro2 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi0.inos < pmaxino, fi2[ndx4.keys, ax].inos < jmaxino0, inv(gstore \ jro), inv(gstore2 \ jro0), inv(gstore0), key-cons(ndx1), key-cons(ndx4), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi0), refsize-cons(gstore, range fi2[ndx4.keys, ax]), ri-inj(fi2), ri-inj(fi0), ri-inj(fi2[ndx4.keys, ax]), pmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore, fi2.lebs ⊆ dom gstore2, fi0.lebs ⊆ dom gstore0, ndx1.keys.toSet ⊆ dom fi2, ndx4.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi2[ndx4.keys, ax].lebs ⊆ dom gstore, ndx2.keys.toSet ⊆ dom fi2 ∪ ndx4.keys.toSet, range fi2[ndx4.keys, ax] ⊆ dom nodes(gstore ↓, jro), dom gstore2 ⊆ dom gstore, jvalid ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), err = ESUCCESS → ndx1 = ndx2, err = ESUCCESS ∨ ⌊err⌋ ⊦ jmaxino = 0, jmaxino0 = 0, pmaxino = 0, dups(ndx1.keys), dups(ndx4.keys), dups(ndx4.keys + ndx1.keys), dups(nx), dups(ax), dups(nx1), ∃ ax0, ndx0, ndx. ndx4 + ndx1 = ndx0 + ndx ∧ (err = ESUCCESS → ndx = []) ∧ new(ax0, nodes(gstore2 ↓, jro0)) ∧ # ax0 = # ndx0 ∧ ¬ dups(ax0) ∧ fi2[ndx4.keys, ax] = fi2[ndx0.keys, ax0] ∧ nodes(gstore ↓, jro) = nodes(gstore2 ↓, jro0)[ax0, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx1, gstore2 ↓) + ax0, err = ESUCCESS ∧ ndx2 ≠ []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ 0 ↔ m = 0; (s)%a: ⊦ ¬ dups(kx + kx0) → ¬ dups(kx) ∧ ¬ dups(kx0); (forward) from specification list-dup[key-list-set]%sub-trans: ⊦ ns ⊆ ns0 ∧ ns0 ⊆ ns1 → ns ⊆ ns1; (forward) from specification set-basic[nat-set]%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ ns < n ∧ n ≤ m → (ns < m ↔ true); (ss)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)% ⊦ key-cons(ndx0 + ndx1) ↔ key-cons(ndx0) ∧ key-cons(ndx1); (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%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 ∪ ks0 ⊆ ks1 ↔ ks ⊆ ks1 ∧ ks0 ⊆ ks1; (ws)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ (kx + kx0).toSet = kx.toSet ∪ kx0.toSet; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]% ⊦ (ndx0 + ndx1).keys = ndx0.keys + ndx1.keys; (s)%# kx = # ax ⊦ dom ri[kx, ax] = dom ri ∪ kx.toSet; (s)% ⊦ # ndx.keys = # ndx; (s)