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Proof step 8 from proof uniquelen (previous step)

∀ ay. (∀ a. a ∈ ax0 ↔ a ∈ ay) ∧ unique_al(ax0) ∧ unique_al(ay) → # ax0 = # ay, ∀ a. a ∈ p + ax0 ↔ a ∈ ay, unique_al(p + ax0), unique_al(ay) ⊦ #(p + ax0) = # ay

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
unique_al(ay), unique_al(p ' + ax0), ∀ ay. (∀ a. a ∈ ax0 ↔ a ∈ ay) ∧ unique_al(ax0) ∧ unique_al(ay) → # ax0 = # ay, ∀ a. a ∈ p ' ∨ a ∈ ax0 ↔ a ∈ ay ⊦ # ax0 + 1 = # ay

Rule argument

Additional information

Used simplifier rules: inapp: ⊦ a ∈ ax + ay ↔ ¬ ¬(a ∈ ax ∨ a ∈ ay);%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclista]%succ: ⊦ m +1 = m + 1; from specification nat-basic2%len-05: ⊦ #(p ' + ax) = (# ax)+1; from specification list[assoclista]%c: ⊦ p + ax = p ' + ax; from specification list[assoclista]