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Proof step 12 from proof lenequal (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# ax0 = # ay0 + # az, unique_al(ay0 + (a × d)' + az), unique_al(ax0), a0 ∈ ax0, ∀ a0. a0 ∈ ax0 → a0 ∈ ay0 ∨ a0 ∈ az, b ∈ ay0 ∨ b ∈ az ⊦ b = a, b ∈ ax0, a ∈ ax0, a ∈ ay0, a ∈ az, a0 ∈ ay0, a0 ∈ 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;%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclist]% ⊦ #(ax + ax0) = # ax + # ax0; (s)