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Proof step 58 from proof inv-gc (previous step)

# lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), ndx = nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)], remove-refsize0(gstore1) = gstore1, elems nx ∩ jro0 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0, jmaxino ≠ 0, m0 ≠ 0, pmaxino ≠ 0, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, inv(gstore2 \ jro0), inv(gstore1), inv(groupblock(gndx0, lax, m0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, ¬ dups(nx), ¬ n1 ∈ nx, ¬ n1 ∈ jro0, jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0) ⊦ ⟪gjournal_gc_copy#(jvalid1, fi1, gstore1, pmaxino, p_os; ndx, jvalid4, jmaxino0, jmaxino, fi2, jro0, gstore2, nx, jvalid; err); if err ≠ ESUCCESS then debug#("gjournal: failed to copy nodes of LEB " + n1.toString + " to journal head during GC"); if err = ESUCCESS then index_sync#(fi2, fi1, jro0, gstore2, gstore1, nx, pmaxino, p_os; ; jvalid, err); if err = ESUCCESS then index_deallocate_gnd#(n1, fi2, fi1, gstore1, nx, pmaxino, p_os, jvalid; jro0, gstore2; err)⟫ ( jro1 < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi2.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid4 ∧ nx ≠ [] → valid-journal-head(nx, gstore2, jro0)) ∧ fi2.lebs ⊆ dom gstore2 ∧ refsize-cons(gstore2, range fi2) ∧ inv(gstore2 \ jro0) ∧ elems nx ∩ jro0 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ jro0 ∧ ri-inj(fi2))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: inv-gc-copy seq: jro < jmaxino, p_os < pmaxino, pmaxino ≤ jmaxino, fi.inos < jmaxino, fi0.inos < pmaxino, jmaxino ≠ 0, pmaxino ≠ 0, jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0), fi.lebs ⊆ dom gstore, fi0.lebs ⊆ dom gstore0, refsize-cons(gstore, range fi), refsize-cons(gstore0, range fi0), inv-journal(nx, gstore, gstore0, jro0), ri-inj(fi), ri-inj(fi0), ndx.keys.toSet ⊆ dom fi, ¬ dups(ndx.keys), range fi ⊆ dom nodes(gstore ↓, jro0), key-cons(ndx), jmaxino0 = jmaxino, gstore1 = gstore, nx0 = nx, ndx2 = ndx, jro1 = jro0, fi1 = fi ⊦ ⟪gjournal_gc_copy# (jvalid0, fi0, gstore0, pmaxino, p_os ; ndx, jvalid, jmaxino1, jmaxino, fi, jro0, gstore, nx, jvalid1 ; err)⟫ ( jro < jmaxino ∧ pmaxino ≤ jmaxino ∧ fi.inos < jmaxino ∧ jmaxino ≠ 0 ∧ (jvalid ∧ nx ≠ [] → valid-journal-head(nx, gstore, jro0)) ∧ fi.lebs ⊆ dom gstore ∧ refsize-cons(gstore, range fi) ∧ inv-journal(nx, gstore, gstore0, jro0) ∧ ri-inj(fi) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ jmaxino0 ≤ jmaxino ∧ dom gstore1 ⊆ dom gstore ∧ (nx.toSet \ nx0.toSet) ∩ dom gstore1 = ∅ ∧ (∃ ax, ndx0, ndx1. ndx2 = ndx0 + ndx1 ∧ (err = ESUCCESS → ndx1 = []) ∧ new(ax, nodes(gstore1 ↓, jro1)) ∧ # ax = # ndx0 ∧ ¬ dups(ax) ∧ fi = fi1[ndx0.keys, ax] ∧ nodes(gstore ↓, jro0) = nodes(gstore1 ↓, jro1)[ax, ndx0] ∧ abs-log(nx, gstore ↓) = abs-log(nx0, gstore1 ↓) + ax)) subst: [p_os, pmaxino, gstore0, fi0, jvalid0, jvalid1, nx, gstore, jro0, fi, jmaxino, jmaxino1, jvalid, ndx, err, jro, jmaxino0, gstore1, nx0, jro1, fi1, ndx2] → [p_os, pmaxino, gstore1, fi1, jvalid1, jvalid, nx, gstore2, jro0, fi2, jmaxino, jmaxino0, jvalid4, ndx, err, jro1, jmaxino, gstore2, nx, jro0, fi2, ndx] flags: <all paths>

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