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Proof step 158 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 ↓), 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(groupblock(gndx0 + gndx, lax0 + lax, m0)), inv(groupblock(gndx0, lax0, m0)), inv-flashsize(gndx, lax), refsize-cons(gstore3, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore2, range fi2), refsize-cons(gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], 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) ⊦ gndx = [], nx0 = [], pmaxino = 0, dups(lax), dups(nx0), dups(nx1), new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1)) ∧ 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] ∧ 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) ∧ valid-journal-head(nx0, gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], jro0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 159:
# gndx = # lax, # 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(gstore0) = gstore0, elems nx1 ∩ jro1 = ∅, (nx0.toSet \ nx1.toSet) ∩ dom gstore2 = ∅, elems nx0 ∩ jro0 = ∅, dom gstore0 ∪ elems nx1 = dom gstore2 ∪ jro1, dom gstore0 ∪ elems nx0 = dom gstore3 ∪ jro0, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(groupblock(gndx0, lax0, m0)), inv(groupblock(gndx0 + gndx, lax0 + lax, m0)), inv(gstore0), inv(gstore2 \ jro1), inv(gstore3 \ jro0), inv-flashsize(gndx, lax), refsize-cons(gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], range fi2), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore3, range fi2), ri-inj(fi2), ri-inj(fi1), transaction(ndx, gndx), valid-journal-head(nx0, gstore3, jro0), nx0.last ∈ gstore3, pmaxino ≤ jmaxino1, fi2.lebs ⊆ dom gstore3, fi2.lebs ⊆ dom gstore2, fi1.lebs ⊆ dom gstore0, dom gstore2 ⊆ dom gstore3, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ gndx = [], nx0 = [], pmaxino = 0, dups(nx1), dups(nx0), dups(lax), new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1)) ∧ nodes(gstore3 ↓[nx0.last, groupblock(prefixn(# lax0 + # lax, gndx0 + gndx), lax0 + lax, m0)], jro0) = nodes(gstore2 ↓, jro1)[lax.to-adr(nx0.last), ndx] ∧ abs-log(nx0.butlast, gstore3 ↓) + lax0.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) ∧ valid-journal-head(nx0, gstore3[nx0.last, groupblock(gndx0 + gndx, lax0 + lax, m0)], jro0)

Rule argument

Additional information

Used simplifier rules: ⊦ ax + ax0 = ax1 + ax0 ↔ ax = ax1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ (lax0 + lax1).to-adr(n) = lax0.to-adr(n) + lax1.to-adr(n); (s)%# lax ≤ m ⊦ prefixn(m, lax) = lax; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ #(lax + lax0) = # lax + # lax0; (s)