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Proof step 10 from proof lenle (previous step)

unique_al(ax0.tail), a ∈ ay, # ay ≤ # ax0, ∀ a0. a0 ∈ ax0 → a0 ∈ ay ⊦ ax0 = [], a ∈ ax0, ax0.head.1 ∈ ax0.tail, ∃ ay0. # ay0 < # ax0 ∧ (∀ a. a ∈ ax0 → a ∈ ay0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ a ∈ ax ↔ (∃ d, ay, az. ax = ay + (a × d)' + az)
Proof step 12:
unique_al(ax0.tail), # ay ≤ # ax0, ∀ a0. a0 ∈ ax0 → a0 ∈ ay, ∃ d, ay0, az. ay = ay0 + (a × d)' + az ⊦ ax0 = [], ax0.head.1 ∈ ax0.tail, a ∈ ax0, ∃ ay0. # ay0 < # ax0 ∧ (∀ a. a ∈ ax0 → a ∈ ay0)

Rule argument

spec: <toplevel> name: ex seq: ⊦ a ∈ ax ↔ (∃ d, ay, az. ax = ay + (a × d)' + az) subst: [ax, a] → [ay, a] flags: <all paths>

Additional information

Used terms: ay, a