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Proof step 63 from proof inv-addn (previous step)

# lax = # gndx, # gndx0 = # lax1, gstore3[nx0.last] = groupblock(gndx0, lax1, 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, nx0 ≠ [], pmaxino ≠ 0, fi1.inos < pmaxino, fi2.inos < jmaxino1, p_os < pmaxino, inv(groupblock(gndx0, lax1, m)), inv(gstore3 \ jro0), inv(gstore2 \ jro1), inv(gstore0), inv(groupblock(gndx0 + gndx, lax1 + lax, m)), inv-flashsize(gndx, lax), 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, ¬ dups(lax), ¬ dups(nx1), ¬ dups(nx0), jvalid4 ∧ nx1 ≠ [] → valid-journal-head(nx1, gstore2, jro1) ⊦ ⟪index_sync# (fi2, fi1, jro0, gstore3[nx0.last, gstore3[nx0.last, gstore3[nx0.last].gndlist:= (gndx0 + gndx)][nx0.last].ladrlist:= (lax1 + lax)], gstore0, nx0, pmaxino, p_os ; ; jvalid, err0)⟫ ( valid-journal-head(nx0, gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax1 + lax)], jro0) ∧ refsize-cons(gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax1 + lax)], range fi2) ∧ nodes-cons(lax.to-adr(nx0.last), ndx, gstore3[nx0.last, (gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax1 + lax)], jro0) ∧ abs-log(nx0.butlast, gstore3 ↓) + prefixn((gndx = [] ⊃ # lax1;# lax1 + # gndx), lax1 + lax).to-adr(nx0.last) = abs-log(nx1, gstore2 ↓) + lax.to-adr(nx0.last) ∧ nodes(gstore3 ↓[nx0.last, ((gstore3[nx0.last].gndlist:= (gndx0 + gndx)).ladrlist:= (lax1 + lax))↓], jro0) = nodes(gstore2 ↓, jro1)[lax.to-adr(nx0.last), ndx] ∧ new(lax.to-adr(nx0.last), nodes(gstore2 ↓, jro1)))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: index-asm name: inv-sync seq: inv-journal(nx, gstore, gstore0, ginval), ri-inj(fi), ri-inj(fi0) ⊦ ⟪index_sync# (fi, fi0, ginval, gstore, gstore0, nx, maxino, ginval0 ; ; syn, err)⟫ true subst: [ginval0, maxino, nx, gstore0, gstore, ginval, fi0, fi, err, syn] → [p_os, pmaxino, nx0, gstore0, gstore3 [nx0.last, gstore3 [nx0.last, gstore3[nx0.last].gndlist:= (gndx0 + gndx) ] [nx0.last ] .ladrlist:= (lax1 + lax) ], jro0, fi1, fi2, err0, jvalid] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ls-inv-reduce-jnlhead: ⊦ inv(gstore \ ns) ∧ valid-journal-head(nx, gstore, ns) ∧ nx ≠ [] → (inv(gstore[nx.last, gblock] \ ns) ↔ inv(gblock));% ⊦ gstore[n, gblock][n] = gblock; (s)%⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)% ⊦ n ∈ gstore → dom gstore ++ n = dom gstore; (s)%⊦ groupblock(gndx, lax, m).gndlist:= gndx0 = groupblock(gndx0, lax, m); (s)%⊦ groupblock(gndx, lax, m).ladrlist:= lax0 = groupblock(gndx, lax0, m); (s)% ⊦ inv(groupblock(gndx, lax, m0)) → inv(groupblock(gndx, lax, n0)); (s)