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

# lax = # gndx, gstore3[nx0.last] = groupblock(gndx0, lax0, m), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro1 = ∅, dom gstore0 ∪ elems nx0 = dom gstore3 ∪ jro0, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore0), inv((gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax)), inv(gstore3[nx0.last]), inv-flashsize(gndx, lax), refsize-cons(gstore3, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, dom gstore2 ⊆ dom gstore3, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ ⟪index_sync# (fi2, fi1, jro0, gstore3 [nx0.last, gstore3[nx0.last, gstore3[nx0.last].gndlist:= (gndx0 + gndx)][nx0.last] .ladrlist:= (gstore3[nx0.last, gstore3[nx0.last].gndlist:= (gndx0 + gndx)][nx0.last].ladrlist + lax) ], gstore0, nx0, pmaxino, p_os ; ; jvalid, err0)⟫ ( valid-journal-head(nx0, gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax)], jro0) ∧ refsize-cons(gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax)], range fi2) ∧ nodes-cons(lax.to-adr(nx0.last), ndx, gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax)], jro0) ∧ abs-log(nx0.butlast, gstore3 ↓) + ((gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax))↓.ladrlist.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) + lax.to-adr(nx0.last) ∧ nodes(gstore3 ↓[nx0.last, ((gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax))↓], jro0) = nodes(gstore2 ↓, jro1)[lax.to-adr(nx0.last), ndx] ∧ new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1))), nx0 = [], pmaxino = 0, dups(lax), dups(lax0), dups(nx1), dups(nx0), dups(lax0 + lax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
# lax = # gndx, # gndx0 = # lax0, gstore3[nx0.last] = groupblock(gndx0, lax0, m), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore0) = gstore0, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro1 = ∅, dom gstore0 ∪ elems nx0 = dom gstore3 ∪ jro0, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, nx0 ≠ [], pmaxino ≠ 0, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(groupblock(gndx0, lax0, m)), inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore0), inv(groupblock(gndx0 + gndx, lax0 + lax, m)), inv-flashsize(gndx, lax), refsize-cons(gstore3, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, dom gstore2 ⊆ dom gstore3, fi1.lebs ⊆ dom gstore0, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, ¬ dups(lax), ¬ dups(nx1), ¬ dups(nx0), jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ ⟪index_sync# (fi2, fi1, jro0, gstore3 [nx0.last, gstore3[nx0.last, gstore3[nx0.last].gndlist:= (gndx0 + gndx)][nx0.last] .ladrlist:= (gstore3[nx0.last, gstore3[nx0.last].gndlist:= (gndx0 + gndx)][nx0.last].ladrlist + lax) ], gstore0, nx0, pmaxino, p_os ; ; jvalid, err0)⟫ ( valid-journal-head(nx0, gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax)], jro0) ∧ refsize-cons(gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax)], range fi2) ∧ nodes-cons(lax.to-adr(nx0.last), ndx, gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax)], jro0) ∧ abs-log(nx0.butlast, gstore3 ↓) + ((gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax))↓.ladrlist.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) + lax.to-adr(nx0.last) ∧ nodes(gstore3 ↓[nx0.last, ((gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax0 + lax))↓], jro0) = nodes(gstore2 ↓, jro1)[lax.to-adr(nx0.last), ndx] ∧ new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1)))

Rule argument

Additional information

Used simplifier rules: lf-inv-append-sizes: ⊦ # gndx1 = # lax1 ∧ inv(groupblock(gndx0 + gndx1, lax0 + lax1, m)) → # gndx0 = # lax0;%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ inv(groupblock(gndx, lax, m0)) → ¬ dups(lax); (s)% ⊦ inv(groupblock(gndx, lax0 + lax1, m0)) → ¬ dups(lax0); (s)%⊦ groupblock(gndx, lax, m).ladrlist:= lax0 = groupblock(gndx, lax0, m); (s)%⊦ groupblock(gndx, lax, m).gndlist:= gndx0 = groupblock(gndx0, lax, m); (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]