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Proof step 10 from proof lenequal (previous step)

# ax0 = # ay0 + # az, unique_al(ay0 + (a × d)' + az), unique_al(ax0), ∀ ay0, b0. unique_al(ay0) ∧ # ax0 = # ay0 ∧ (∀ a. a ∈ ax0 → a ∈ ay0) ∧ b0 ∈ ay0 → b0 ∈ ax0, ∀ a0. a0 ∈ ax0 → a0 ∈ az ∨ a0 ∈ ay0 ⊦ b = a, a ∈ ax0, b ∈ ax0, a ∈ ay0, a ∈ az, ¬ b ∈ az ∧ ¬ b ∈ ay0

User applied rule all left

And obtained the following new goals

Proof step 11:
# ax0 = # ay0 + # az, unique_al(ay0 + (a × d)' + az), unique_al(ax0), unique_al(ay0 + az) ∧ # ax0 = #(ay0 + az) ∧ (∀ a. a ∈ ax0 → a ∈ ay0 + az) ∧ b ∈ ay0 + az → b ∈ ax0, ∀ a0. a0 ∈ ax0 → a0 ∈ az ∨ a0 ∈ ay0 ⊦ b = a, a ∈ ax0, b ∈ ax0, a ∈ ay0, a ∈ az, ¬ b ∈ az ∧ ¬ b ∈ ay0

Rule argument

pos: left 4 terms: ay0 + az, b abort: F discard: T computed: F

Additional information

Used terms: ay0 + az, b