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Proof step 3 from proof last-notin-butlast-nodups (previous step)

nx.last ∈ nx.butlast ⊦ nx = [], dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ nx = [] ↔ ¬(∃ nx0, n. nx = nx0 + n ')

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: ⊦ (nx + n ').last = n; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ (nx + n ').butlast = nx; (s)% ⊦ n ∈ nx → dups(nx + n '); (s) Used terms: nx