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Proof step 4 from proof app (previous step)

unique_al(p ' + ay) ⊦ ay = [], ¬ ay.first.1 ∈ ay.rest ∧ unique_al(ay.rest)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: k-unique-r seq: ⊦ unique_al(ay) ↔ ay = [] ∨ ¬ ay.first.1 ∈ ay.rest ∧ unique_al(ay.rest) subst: [ay] → [p ' + ay] flags: rewrite, current

Additional information

Used simplifier rules: k-unique-r: ⊦ unique_al(ay) ↔ ay = [] ∨ ¬ ay.first.1 ∈ ay.rest ∧ unique_al(ay.rest);%e-01: ⊦ p ' + ax ≠ []; from specification list[assoclista]%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclista]%c-08: ⊦ (p ' + ax).first = p; from specification list[assoclista]%c-07: ⊦ (p ' + ax).rest = ax; from specification list[assoclista] Used terms: p ' + ay