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Proof step 9 from proof disj-write (previous step)

n < m, n < # asar, m ≤ # asar, ∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n0] ∩ asar[n1] = ∅ ⊦ (∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n, as][n0] ∩ asar[n, as][n1] = ∅) ↔ (∀ n0. n0 ≠ n ∧ n0 < m → asar[n0] ∩ as = ∅)

User applied rule case distinction

And obtained the following new goals

Proof step 10:
n < # asar, n < m, m ≤ # asar, ∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n0] ∩ asar[n1] = ∅, ∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n, as][n0] ∩ asar[n, as][n1] = ∅ ⊦ ∀ n0. n0 ≠ n ∧ n0 < m → asar[n0] ∩ as = ∅
Proof step 12:
n < # asar, n < m, m ≤ # asar, ∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n0] ∩ asar[n1] = ∅, ∀ n0. n0 ≠ n ∧ n0 < m → asar[n0] ∩ as = ∅ ⊦ ∀ n0, n1. n0 < m ∧ n1 < m ∧ n0 ≠ n1 → asar[n, as][n0] ∩ asar[n, as][n1] = ∅

Rule argument

pos: right 1

Proof step 9 from proof disj-write (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information