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Proof step 144 from proof inv-gc (previous step)

# ax = # referenced-adrs(lax.to-adr(n1), fi2), # lax = # gndx0, gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, err = err0, nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx1 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro = ∅, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, jro1 < jmaxino, p_os < pmaxino, fi2.inos < jmaxino, fi1.inos < pmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, jro1 < jmaxino0, inv(groupblock(gndx0, lax, m0)), inv(gstore1), inv(gstore2 \ jro0), inv(gstore3 \ jro), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore2, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore3, range fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2), ri-inj(fi1), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), n1 ∈ gstore1, n1 ∈ gstore2, pmaxino ≤ jmaxino, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino0, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore1, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), dom gstore2 ⊆ dom gstore3, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪fi := fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]; if err = ESUCCESS then index_deallocate_gnd#(n1, fi, fi1, gstore1, nx0, pmaxino, p_os, jvalid; jro, gstore3; err)⟫ ( (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro)) ∧ fi.lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi) ∧ inv(gstore3 \ jro) ∧ elems nx0 ∩ jro = ∅ ∧ dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro), err = ESUCCESS, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dups(nx1), dups(ax), dups(nx0), dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), n1 ∈ nx1, n1 ∈ jro0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 145:
# lax = # gndx0, # ax = # referenced-adrs(lax.to-adr(n1), fi2), gstore2[n1] = groupblock(gndx0, lax, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓) + ax, err = err0, fi = fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax], nodes(gstore3 ↓, jro) = nodes(gstore2 ↓, jro0)[ax, nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)]], remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro0 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro0, jro1 < jmaxino0, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].inos < jmaxino0, fi1.inos < pmaxino, fi2.inos < jmaxino, p_os < pmaxino, jro1 < jmaxino, inv(gstore3 \ jro), inv(gstore2 \ jro0), inv(gstore1), inv(groupblock(gndx0, lax, m0)), new(ax, nodes(gstore2 ↓, jro0)), refsize-cons(gstore3, range fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-cons(fi2, nodes(gstore2 ↓, jro0)), ri-inj(fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax]), ri-inj(fi1), ri-inj(fi2), n1 ∈ gstore2, n1 ∈ gstore1, pmaxino ≤ jmaxino0, jmaxino ≤ jmaxino0, pmaxino ≤ jmaxino, fi2[nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys, ax].lebs ⊆ dom gstore3, dom gstore2 ⊆ dom gstore3, range fi2 ⊆ dom nodes(gstore2 ↓, jro0), fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro0), jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪if err = ESUCCESS then index_deallocate_gnd#(n1, fi, fi1, gstore1, nx0, pmaxino, p_os, jvalid; jro, gstore3; err)⟫ ( (jvalid0 ∧ nx0 ≠ [] → valid-journal-head(nx0, gstore3, jro)) ∧ fi.lebs ⊆ dom gstore3 ∧ refsize-cons(gstore3, range fi) ∧ inv(gstore3 \ jro) ∧ elems nx0 ∩ jro = ∅ ∧ dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro), err = ESUCCESS, jmaxino = 0, jmaxino0 = 0, m0 = 0, pmaxino = 0, dups(nodes(gstore2 ↓, jro0)[referenced-adrs(lax.to-adr(n1), fi2)].keys), dups(nx0), dups(ax), dups(nx1), n1 ∈ jro0, n1 ∈ nx1

Proof step 144 from proof inv-gc (previous step)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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