Proof step 30 from proof orderedle-all (previous step)

User applied rule case distinction

And obtained the following new goals

• Proof step 31:

  ∀ m, n. m ≤ n ∧ ¬ 1 + # y < n → ¬ (a ' + a0 ' + y)[n] < (a ' + a0 ' + y)[m] ⊦ ordered≤(a0 ' + y), ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m], ¬ a0 < a ∧ ordered≤(a0 ' + y)

• Proof step 33:

  ordered≤(a0 ' + y), ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m], ∀ m, n. m ≤ n ∧ ¬ 1 + # y < n → ¬ (a ' + a0 ' + y)[n] < (a ' + a0 ' + y)[m] ⊦ ¬ a0 < a ∧ ordered≤(a0 ' + y)

Rule argument

Additional information