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Proof step 39 from proof inv-addn (previous step)

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, # lax < # gndx, p_os < pmaxino, fi2.inos < jmaxino1, fi1.inos < pmaxino, inv(gstore3[nx0.last]), inv((gstore3[nx0.last].gndlist:= (gstore3[nx0.last].gndlist + prefixn(# lax, gndx))).ladrlist:= (gstore3[nx0.last].ladrlist + lax)), inv(gstore0), inv(gstore2 \ jro1), inv(gstore3 \ jro0), inv-flashsize(prefixn(# lax, gndx), lax), refsize-cons(gstore2, range fi2), refsize-cons(gstore0, range fi1), refsize-cons(gstore3, range fi2), refsize-cons (gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gstore3[nx0.last].gndlist + prefixn(# lax, gndx))).ladrlist:= (gstore3[nx0.last].ladrlist + lax)], 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, ⌊err0⌋ , jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ # lax = # gndx, gndx = [], nx0 = [], pmaxino = 0, dups(lax), dups(gstore3[nx0.last].ladrlist), dups(nx1), dups(nx0), dups(gstore3[nx0.last].ladrlist + lax), nodes (gstore3 ↓ [nx0.last, ((gstore3[nx0.last].gndlist:= (gstore3[nx0.last].gndlist + prefixn(# lax, gndx))).ladrlist:= (gstore3[nx0.last].ladrlist + lax))↓ ], jro0) = nodes(gstore2 ↓, jro1) ∧ abs-log(nx0.butlast, gstore3 ↓) + ((gstore3[nx0.last].gndlist:= (gstore3[nx0.last].gndlist + prefixn(# lax, gndx))).ladrlist:= (gstore3[nx0.last].ladrlist + lax))↓.ladrlist .to-adr (nx0.last ) = abs-log(nx1, gstore2 ↓)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
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, # lax < # gndx, inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore0), inv((gstore3[nx0.last].gndlist:= (gndx0 + prefixn(# lax, gndx))).ladrlist:= (lax0 + lax)), inv(gstore3[nx0.last]), inv-flashsize(prefixn(# lax, gndx), lax), refsize-cons(gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + prefixn(# lax, gndx))).ladrlist:= (lax0 + lax)], range fi2), 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, ⌊err0⌋ , jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ # lax = # gndx, gndx = [], nx0 = [], pmaxino = 0, dups(lax0 + lax), dups(nx0), dups(nx1), dups(lax0), dups(lax), nodes(gstore3 ↓[nx0.last, ((gstore3[nx0.last].gndlist:= (gndx0 + prefixn(# lax, gndx))).ladrlist:= (lax0 + lax))↓], jro0) = nodes(gstore2 ↓, jro1) ∧ abs-log(nx0.butlast, gstore3 ↓) + ((gstore3[nx0.last].gndlist:= (gndx0 + prefixn(# lax, gndx))).ladrlist:= (lax0 + lax))↓.ladrlist.to-adr(nx0.last) = abs-log(nx1, gstore2 ↓)

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