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Proof step 129 from proof inv-addn (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 130:
# lax = # gndx, # lax0 = # gndx0, 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, gstore3[nx0.last] ↓ = groupblock(gndx0, lax0, m), 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(gstore3[nx0.last]), 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) ⊦ gndx = [], 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 ↓) + lax0.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) ∧ new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1))

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m] → [gstore3[nx0.last] ↓, gndx0, lax0, m]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: gstore3[nx0.last] ↓, gndx0, lax0, m