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Proof step 202 from proof inv-gc-copy (previous step)

# 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 ≠ []

User applied rule cut formula

And obtained the following new goals

Proof step 203:
# ax = # ndx4, ndx4 + ndx1 = ndx0 + ndx2, abs-log(nx, gstore ↓) = abs-log(nx1, gstore2 ↓) + ax, err = ESUCCESS, nodes(gstore ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx4], remove-refsize0(gstore0) = gstore0, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore0 ∪ elems nx = dom gstore ∪ jro, fi2[ndx4.keys, ax].inos < jmaxino0, fi0.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro2 < jmaxino, inv(gstore0), inv(gstore2 \ jro0), inv(gstore \ jro), key-cons(ndx4), key-cons(ndx1), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore, range fi2[ndx4.keys, ax]), refsize-cons(gstore0, range fi0), refsize-cons(gstore2, range fi2), ri-inj(fi2[ndx4.keys, ax]), ri-inj(fi0), ri-inj(fi2), jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, pmaxino ≤ jmaxino0, dom gstore2 ⊆ dom gstore, range fi2[ndx4.keys, ax] ⊆ dom nodes(gstore ↓, jro), ndx2.keys.toSet ⊆ dom fi2 ∪ ndx4.keys.toSet, fi2[ndx4.keys, ax].lebs ⊆ dom gstore, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), ndx4.keys.toSet ⊆ dom fi2, ndx1.keys.toSet ⊆ dom fi2, fi0.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore, err = ESUCCESS → ndx1 = ndx2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), jvalid ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), err = ESUCCESS ∨ ⌊err⌋ ⊦ jmaxino = 0, jmaxino0 = 0, pmaxino = 0, dups(nx1), dups(ax), dups(nx), dups(ndx4.keys + ndx1.keys), dups(ndx4.keys), dups(ndx1.keys), ∃ 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 ≠ []
Proof step 205:
# 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, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, elems nx ∩ jro = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore0 ∪ elems nx = dom gstore ∪ jro, fi2[ndx4.keys, ax].inos < jmaxino0, fi0.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro2 < jmaxino, inv(gstore0), inv(gstore2 \ jro0), inv(gstore \ jro), key-cons(ndx4), key-cons(ndx1), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore, range fi2[ndx4.keys, ax]), refsize-cons(gstore0, range fi0), refsize-cons(gstore2, range fi2), ri-inj(fi2[ndx4.keys, ax]), ri-inj(fi0), ri-inj(fi2), jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, pmaxino ≤ jmaxino0, dom gstore2 ⊆ dom gstore, range fi2[ndx4.keys, ax] ⊆ dom nodes(gstore ↓, jro), ndx2.keys.toSet ⊆ dom fi2 ∪ ndx4.keys.toSet, fi2[ndx4.keys, ax].lebs ⊆ dom gstore, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), ndx4.keys.toSet ⊆ dom fi2, ndx1.keys.toSet ⊆ dom fi2, fi0.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore, err = ESUCCESS → ndx1 = ndx2, jvalid1 ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro), jvalid ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), err = ESUCCESS ∨ ⌊err⌋ ⊦ err = ESUCCESS, jmaxino = 0, jmaxino0 = 0, pmaxino = 0, dups(nx1), dups(ax), dups(nx), dups(ndx4.keys + ndx1.keys), dups(ndx4.keys), dups(ndx1.keys), ∃ 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

fma: err = ESUCCESS

Additional information

Used formulas: err = ESUCCESS