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Proof step 141 from proof inv-gc-copy (previous step)

# ax = # ndx1, # ax1 = # ndx + 1, LEB_SIZE = n1 + n0, abs-log(nx0, gstore0 ↓) = abs-log(nx0, gstore ↓), abs-log(nx, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, abs-log(nx0, gstore ↓) = abs-log(nx, gstore3 ↓) + ax1, dom gstore0 = dom gstore, nodes(gstore0 ↓, jro3) = nodes(gstore ↓, jro3), nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, ndx1], nodes(gstore ↓, jro3) = nodes(gstore3 ↓, jro)[ax1, nd0 ' + ndx], remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro3 = ∅, (nx0.toSet \ nx.toSet) ∩ dom gstore3 = ∅, elems nx1 ∩ jro0 = ∅, (nx.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx ∩ jro = ∅, dom gstore1 ∪ elems nx0 = dom gstore ∪ jro3, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx = dom gstore3 ∪ jro, fi2[ndx1.keys, ax].inos < jmaxino, fi2[ndx1.keys, ax][nd0.key ' + ndx.keys, ax1].inos < jmaxino, jro2 < jmaxino3, fi2.inos < jmaxino3, p_os < pmaxino, fi2[ndx1.keys, ax].inos < jmaxino0, fi1.inos < pmaxino, inv(gstore0 \ jro3), inv(gstore \ jro3), inv(gstore3[nx.last]), inv(gstore2 \ jro0), inv(gstore1), inv(gstore3 \ jro), key-cons(ndx3), key-cons(ndx), key-cons(ndx1), key-cons(nd0.key, nd0), new(ax, nodes(gstore2 ↓, jro0)), new(ax1, nodes(gstore3 ↓, jro)), nodes-cons(ax1, nd0 ' + ndx, gstore, jro3), refsize-cons(gstore0, range fi2[ndx1.keys, ax][nd0.key ' + ndx.keys, ax1]), refsize-cons(gstore3, range fi2[ndx1.keys, ax]), refsize-cons(gstore2, range fi2), refsize-cons(gstore, range fi2[ndx1.keys, ax]), refsize-cons(gstore1, range fi1), ri-inj(fi2[ndx1.keys, ax][nd0.key ' + ndx.keys, ax1]), ri-inj(fi2), ri-inj(fi2[ndx1.keys, ax]), ri-inj(fi1), nd0.key ∈ fi2, nx.last ∈ gstore3, pmaxino ≤ jmaxino, jmaxino0 ≤ jmaxino, nd0.flashsize ≤ LEB_SIZE, nd0.flashsize + ndx.flashsize ≤ n1, jmaxino3 ≤ jmaxino0, pmaxino ≤ jmaxino3, n0 ≤ LEB_SIZE, nd0.flashsize ≤ n0, pmaxino ≤ jmaxino0, jmaxino3 ≤ jmaxino, fi2[ndx1.keys, ax][nd0.key ' + ndx.keys, ax1].lebs ⊆ dom gstore, dom gstore3 ⊆ dom gstore, fi2[ndx1.keys, ax].lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, ndx1.keys.toSet ⊆ dom fi2, ndx3.keys.toSet ⊆ dom fi2, ndx.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), range fi2[ndx1.keys, ax] ⊆ dom nodes(gstore3 ↓, jro), dom gstore2 ⊆ dom gstore3, fi2.lebs ⊆ dom gstore, dom gstore2 ⊆ dom gstore, fi2[ndx1.keys, ax].lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore1, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore0, jro3), jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid1 → valid-journal-head(nx, gstore3, jro), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore, jro3), ndx3 = [] ∨ n1 < (nd0.flashsize + ndx.flashsize) + ndx3.head.flashsize ⊦ jmaxino = 0, jmaxino0 = 0, jmaxino3 = 0, nx = [], pmaxino = 0, dups(nx0), dups(ndx.keys), dups(ndx1.keys), dups(ndx1.keys + ndx.keys + ndx3.keys), dups(ax), dups(nx), dups(nx1), dups(ndx.keys + ndx3.keys), dups(ndx1.keys + ndx.keys), dups(ndx3.keys), dups(ax1), nd0.key ∈ ndx1.keys, nd0.key ∈ ndx.keys, nd0.key ∈ ndx3.keys, ∃ ax0. new(ax0, nodes(gstore2 ↓, jro0)) ∧ ¬ dups(ax0) ∧ # ax0 = # ndx1 + # ax1 ∧ fi2[ndx1.keys, ax][nd0.key ' + ndx.keys, ax1] = fi2[ndx1.keys + nd0.key ' + ndx.keys, ax0] ∧ nodes(gstore ↓, jro3) = nodes(gstore2 ↓, jro0)[ax0, ndx1 + nd0 ' + ndx] ∧ abs-log(nx0, gstore ↓) = abs-log(nx1, gstore2 ↓) + ax0

User applied rule exists right

And closed the goal!

Rule argument

pos: right 20 terms: ax + ax1 abort: F discard: T computed: F

Additional information

Used simplifier rules: abs-log-simp0: ⊦ ax0 = ax + ax2 → (ax0 = ax1 + ax2 ↔ ax = ax1);% ⊦ new(ax0 + ax1, fs) ↔ new(ax0, fs) ∧ new(ax1, fs); (s)%# ax0 = # ndx ⊦ new(ax1, fs1) ∧ fs1 = fs0[ax0, ndx] → new(ax1, fs0); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%# ax0 = # ndx0 ⊦ ¬ dups(ax0) ∧ ¬ dups(ax1) ∧ new(ax1, fs1) ∧ fs1 = fs0[ax0, ndx0] → ¬ dups(ax0 + ax1); (s)% ⊦ #(ax + ax0) = # ax + # ax0; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # ndx.keys = # ndx; (s)% ⊦ #(key ' + kx) = (# kx)+1; (s)% ⊦ m +1 = m + 1; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]%# kx0 = # ax0, # kx1 = # ax1 ⊦ ri[kx0 + kx1, ax0 + ax1] = ri[kx0, ax0][kx1, ax1]; (s)% ⊦ #(nd ' + ndx) = (# ndx)+1; (s)%a: ⊦ (ndx + ndx0) + ndx1 = ndx + ndx0 + ndx1; from specification list[node-list]%# ax0 = # ndx0, # ax1 = # ndx1 ⊦ fs[ax0 + ax1, ndx0 + ndx1] = fs[ax0, ndx0][ax1, ndx1]; (s) Used terms: ax + ax1