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Proof step 18 from proof uniquelen (previous step)

unique_al(ay0 + (a × d)' + az), unique_al(ax0), unique_al(ay0 + az) ∧ (∀ a. a ∈ ax0 ↔ a ∈ ay0 + az) → # ax0 = #(ay0 + az), ∀ a0. a0 ≠ a → (a0 ∈ ax0 ↔ a0 ∈ ay0 ∨ a0 ∈ az), ∀ ay0. unique_al(ay0) ∧ (∀ a. a ∈ ax0 ↔ a ∈ ay0) → # ax0 = # ay0 ⊦ # ax0 = # ay0 + # az, a ∈ az, a ∈ ay0, a ∈ ax0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
unique_al(ax0), unique_al(ay0 + (a × d)' + az), ∀ ay0. unique_al(ay0) ∧ (∀ a. a ∈ ax0 ↔ a ∈ ay0) → # ax0 = # ay0, ∀ a0. a0 ≠ a → (a0 ∈ ax0 ↔ a0 ∈ ay0 ∨ a0 ∈ az) ⊦ # ax0 = # ay0 + # az, a0 ∈ ax0 ↔ a0 ∈ ay0 ∨ a0 ∈ az, a ∈ ax0, a ∈ ay0, a ∈ az

Rule argument

Additional information

Used simplifier rules: app: ⊦ unique_al(ax + p ' + ay) → unique_al(ax + ay);%inapp: ⊦ a ∈ ax + ay ↔ a ∈ ax ∨ a ∈ ay;% ⊦ #(ax + ax0) = # ax + # ax0; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclist]