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Proof step 19 from proof nodes-transaction (previous step)

# lax1 = # gndx1, # lax = # gndx, gstore[n] = groupblock(gndx, lax, m), gstore[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(n, m2, m3)] = mkgnode(nd, m4, boolvar, boolvar0), transaction(ndx, gndx1), @(m2, m3) ∈ lax1, n ∈ gstore ⊦ nd = nodes(gstore, ginval)[lax1.to-adr(n), ndx][@(n, m2, m3)], dups(lax1), dups(lax), dups(lax + lax1), n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ # ax = # ndx ∧ adr ∈ ax ∧ ¬ dups(ax) → fs[ax, ndx][adr] = ndx[pos(adr, ax)]
Proof step 21:
# lax = # gndx, # lax1 = # gndx1, # lax1.to-adr(n) = # ndx, gstore[n, groupblock(gndx + gndx1, lax + lax1, m0)][@(n, m2, m3)] = mkgnode(nd, m4, boolvar, boolvar0), gstore[n] = groupblock(gndx, lax, m), transaction(ndx, gndx1), n ∈ gstore, @(m2, m3) ∈ lax1, @(n, m2, m3) ∈ lax1.to-adr(n) ⊦ nd = ndx[pos(@(n, m2, m3), lax1.to-adr(n))], dups(lax + lax1), dups(lax), dups(lax1), dups(lax1.to-adr(n)), n ∈ ginval

Rule argument

spec: aubifs-base name: at-write-at seq: ⊦ # ax = # ndx ∧ adr ∈ ax ∧ ¬ dups(ax) → fs[ax, ndx][adr] = ndx[pos(adr, ax)] subst: [adr, ndx, ax, fs] → [@(n, m2, m3), ndx, lax1.to-adr(n), nodes(gstore, ginval)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # lax.to-adr(n) = # lax; (s)% ⊦ # gndx = n ∧ transaction(ndx, gndx) → (# ndx = n ↔ true); (ss)% ⊦ @(m, m0, m1) ∈ lax.to-adr(n) ↔ m = n ∧ @(m0, m1) ∈ lax; (ws)% ⊦ dups(lax.to-adr(n)) ↔ dups(lax); (s) Used terms: @(n, m2, m3), ndx, lax1.to-adr(n), nodes(gstore, ginval)