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Proof step 104 from proof inv-addn (previous step)

# lax0 = # gndx0, # lax = # gndx, gstore3[nx0.last] = groupblock(gndx0, lax0, m0), abs-log(nx0, gstore3 ↓) = abs-log(nx1, gstore2 ↓), 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, jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ gndx = [], nx0 = [], pmaxino = 0, dups(nx0), dups(nx1), dups(lax), new(lax.to-adr(nx0.last), nodes(gstore3 ↓, jro0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: gjournal-abs name: new-adrs-gstore seq: ⊦ ¬ dups(gstore[n].ladrlist + lax) → new(lax.to-adr(n), nodes(gstore, ginval)) subst: [ginval, gstore, n, lax] → [jro0, gstore3 ↓, nx0.last, lax] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ gstore → gstore ↓[n] = gstore[n] ↓; (s)%⊦ groupblock(gndx, lax, m0) ↓ = groupblock (prefixn(valid-group-nodes(gndx), gndx), prefixn(valid-group-nodes(gndx), lax), m0); (s)%⊦ valid-journal-head(nx, gstore, ginval) ∧ nx ≠ [] ∧ gstore[nx.last] = groupblock(gndx, lax, lnum) → valid-group-nodes(gndx) = # gndx; (s)% ⊦ prefixn(# gndx, gndx) = gndx; (s)% ⊦ inv(groupblock(gndx, lax, m0)) → prefixn(# gndx, lax) = lax; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ inv(groupblock(gndx, lax, m0)) → ¬ dups(lax); (s) Used terms: jro0, gstore3 ↓, nx0.last, lax