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Proof step 5 from proof abs-log-write-last (previous step)

⊦ abs-log(nx, gstore[nx.last, groupblock(gndx, lax, m)]) = abs-log(nx.butlast, gstore) + lax.to-adr(nx.last), nx = [], dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list, inst: nat-list-set name: lastdiv-rew seq: ⊦ nx = [] ↔ ¬(∃ nx0, n. nx = nx0 + n ') subst: [nx] → [nx] flags: <all paths>

Additional information

Used simplifier rules: abs-log-append-one: ⊦ abs-log(nx + n ', gstore) = abs-log(nx, gstore) + gstore[n].ladrlist.to-adr(n);%abs-log-change-other: ⊦ ¬ n ∈ nx → abs-log(nx, gstore[n, gblock]) = abs-log(nx, gstore);% ⊦ (nx + n ').last = n; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ groupblock(gndx, lax, m).ladrlist = lax; (s)% ⊦ (nx + n ').butlast = nx; (s)% ⊦ ax + ax0 = ax1 + ax0 ↔ ax = ax1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ dups(nx + n ') ↔ n ∈ nx ∨ dups(nx); (ws) Used terms: nx