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Proof step 189 from proof inv-gc-copy (previous step)

# abs-log(nx0, gstore ↓) = # ndx + 1, abs-log(nx1, gstore2 ↓) = [], abs-log(nx0, gstore ↓) = ax, ax1 = abs-log(nx0, gstore ↓), dom gstore1 = dom gstore3 ∪ jro, fi = fi2, gstore5 = gstore, jmaxino1 = jmaxino0, ndx0 = nd ' + ndx, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0), nodes(gstore ↓, jro3) = nodes(gstore2 ↓, jro0)[abs-log(nx0, gstore ↓), nd ' + ndx], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, nx0.toSet ∩ dom gstore3 = ∅, elems nx0 ∩ jro3 = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = dom gstore ∪ jro3, jmaxino0 ≠ 0, jmaxino3 ≠ 0, pmaxino ≠ 0, fi2.inos < jmaxino3, jro2 < jmaxino3, p_os < pmaxino, fi2.inos < jmaxino0, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(gstore3 \ jro), inv(gstore \ jro3), key-cons(ndx1), key-cons(nd.key, nd), key-cons(ndx), new(abs-log(nx0, gstore ↓), nodes(gstore2 ↓, jro0)), nodes-cons(abs-log(nx0, gstore ↓), nd ' + ndx, gstore, jro3), refsize-cons(gstore3, range fi2), refsize-cons(gstore2, range fi2), refsize-cons(gstore, range fi2), refsize-cons(gstore1, range fi1), ri-inj(fi2), ri-inj(fi1), nd.key ∈ fi2, pmaxino ≤ jmaxino3, jmaxino3 ≤ jmaxino0, nd.flashsize + ndx.flashsize ≤ LEB_SIZE, pmaxino ≤ jmaxino0, dom gstore2 ⊆ dom gstore, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, ndx1.keys.toSet ⊆ dom fi2, ndx.keys.toSet ⊆ dom fi2, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), dom gstore2 ⊆ dom gstore3, dom gstore3 ⊆ dom gstore, fi2.lebs ⊆ dom gstore, fi1.lebs ⊆ dom gstore1, ¬ dups(abs-log(nx0, gstore ↓)), ¬ dups(nx0), ¬ dups(nx1), ¬ dups(ndx.keys + ndx1.keys), ¬ dups(ndx.keys), ¬ dups(ndx1.keys), ¬ nd.key ∈ ndx.keys, ¬ nd.key ∈ ndx1.keys, jvalid7 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore, jro3), ndx1 = [] ∨ LEB_SIZE < (nd.flashsize + ndx.flashsize) + ndx1.head.flashsize ⊦ [gjournal_gc_update_index#(jvalid0, fi1, jro3, gstore1, nx0, pmaxino, p_os, jvalid; ax, ndx0, jmaxino0, fi, gstore)] ( fi2.inos < jmaxino0 ∧ pmaxino ≤ jmaxino0 ∧ fi2[nd.key ' + ndx.keys, ax1].inos < jmaxino0 ∧ jmaxino0 ≠ 0 ∧ (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore, jro3)) ∧ fi2[nd.key ' + ndx.keys, ax1].lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi2[nd.key ' + ndx.keys, ax1]) ∧ inv(gstore \ jro3) ∧ dom gstore1 ∪ elems nx0 = dom gstore ∪ jro3 ∧ ri-inj(fi2[nd.key ' + ndx.keys, ax1]) ∧ fi = fi2[nd.key ' + ndx.keys, ax1] ∧ dom gstore = dom gstore5 ∧ nodes(gstore ↓, jro3) = nodes(gstore5 ↓, jro3) ∧ abs-log(nx0, gstore ↓) = abs-log(nx0, gstore5 ↓) ∧ jmaxino1 ≤ jmaxino0 → jmaxino3 ≤ jmaxino0 ∧ fi2[nd.key ' + ndx.keys, abs-log(nx0, gstore ↓)].inos < jmaxino0 ∧ fi2[nd.key ' + ndx.keys, abs-log(nx0, gstore ↓)].lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi2[nd.key ' + ndx.keys, abs-log(nx0, gstore ↓)]) ∧ ri-inj(fi2[nd.key ' + ndx.keys, abs-log(nx0, gstore ↓)]) ∧ range fi2[nd.key ' + ndx.keys, abs-log(nx0, gstore ↓)] ⊆ dom nodes(gstore ↓, jro3) ∧ dom gstore2 ⊆ dom gstore ∧ new(abs-log(nx0, gstore ↓), nodes(gstore2 ↓, jro0)) ∧ ¬ dups(abs-log(nx0, gstore ↓)) ∧ # abs-log(nx0, gstore ↓) = # ndx + 1 ∧ fi2[nd.key ' + ndx.keys, ax1] = fi2[nd.key ' + ndx.keys, abs-log(nx0, gstore ↓)] ∧ nodes(gstore ↓, jro3) = nodes(gstore2 ↓, jro0)[abs-log(nx0, gstore ↓), nd ' + ndx])

User applied rule skip call

And obtained the following new goals

Rule argument

pos: right 1

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