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Proof step 11 from proof ocs-same-length-all (previous step)

x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a), ∀ a. x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a) ⊦ a0 = a ∧ x0 = mklist(a, # x0) ↔ (∀ b. b = a0 ∨ b ∈ x0 → b = a)

User applied rule case distinction

And obtained the following new goals

Proof step 12:
x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a), a0 = a, x0 = mklist(a, # x0), ∀ a. x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a) ⊦ ∀ b. b = a0 ∨ b ∈ x0 → b = a
Proof step 14:
x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a), ∀ a. x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a), ∀ b. b = a0 ∨ b ∈ x0 → b = a ⊦ a0 = a ∧ x0 = mklist(a, # x0)

Rule argument

pos: right 1

Proof step 11 from proof ocs-same-length-all (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information