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Proof step 117 from proof inv-addn (previous step)

# gndx0 = # lax0, # gndx = # lax, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), gndx = [], nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro1 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro0, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro1, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(groupblock(gndx0, lax0, m0)), inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore1), inv(groupblock(gndx0 + gndx, lax0 + lax, m0)), inv-flashsize(gndx, lax), refsize-cons(gstore3, range fi2), refsize-cons(gstore1, 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 gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, ⌊err0⌋ , jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ nx0 = [], pmaxino = 0, dups(nx0), dups(nx1), dups(lax), valid-journal-head(nx0, gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], jro0) ∧ abs-log(nx0.butlast, gstore3 ↓) + prefixn((gndx = [] ⊃ # lax0;# lax0 + # lax), lax0 + lax).to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) + lax.to-adr(nx0.last) ∧ nodes (gstore3 ↓ [nx0.last, groupblock (prefixn((gndx = [] ⊃ # lax0;# lax0 + # lax), gndx0 + gndx), prefixn((gndx = [] ⊃ # lax0;# lax0 + # lax), lax0 + lax), m0) ], jro0) = nodes(gstore2 ↓, jro1)[lax.to-adr(nx0.last), ndx] ∧ new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 118:
# gndx0 = # lax0, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), nodes(gstore3 ↓, jro0) = nodes(gstore2 ↓, jro1), remove-refsize0(gstore1) = gstore1, elems nx0 ∩ jro0 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx1 ∩ jro1 = ∅, dom gstore1 ∪ elems nx0 = dom gstore3 ∪ jro0, dom gstore1 ∪ elems nx1 = dom gstore2 ∪ jro1, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(groupblock(gndx0, lax0, m0)), inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore1), refsize-cons(gstore3, range fi2), refsize-cons(gstore1, range fi1), refsize-cons(gstore2, range fi2), ri-inj(fi1), ri-inj(fi2), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, dom gstore2 ⊆ dom gstore3, fi1.lebs ⊆ dom gstore1, fi2.lebs ⊆ dom gstore2, fi2.lebs ⊆ dom gstore3, ⌊err0⌋ , jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ nx0 = [], pmaxino = 0, dups(nx0), dups(nx1), abs-log(nx0.butlast, gstore3 ↓) + lax0.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) ∧ nodes(gstore3 ↓[nx0.last, groupblock(gndx0, lax0, m0)], jro0) = nodes(gstore2 ↓, jro1)

Rule argument

Additional information

Used simplifier rules: ⊦ new([], fs); (s)% ⊦ fs[[], []] = fs; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + [] = ax; (s)% ⊦ ([]).to-adr(n) = []; (s)% ⊦ gstore[n] = gblock ∧ n ∈ gstore → gstore[n, gblock] = gstore; (s)% ⊦ ¬ dups([]); (s)% ⊦ inv(groupblock(gndx, lax, m0)) → inv(groupblock(gndx, lax, n0)); (s)% ⊦ lax + [] = lax; (s)%# gndx ≤ m ⊦ prefixn(m, gndx) = gndx; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ prefixn(# lax, lax) = lax; (s)%n ≤ # lax ⊦ prefixn(n, lax + lax0) = prefixn(n, lax); (s)% ⊦ ¬ n < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx + [] = gndx; (s)% ⊦ inv-flashsize([], lax) ↔ lax = []; (s)% ⊦ transaction(ndx, []) ↔ ndx = []; (s)% ⊦ # lax = 0 ↔ lax = []; (s)% ⊦ # [] = 0; (s)