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Proof step 9 from proof id-circle-subarray-concrete-below (previous step)

# avol = # avol0, n1 < m0, n0 < n, n + m + m0 ≤ # avol0, ∀ m. m < # avol0 ∧ m ≠ n0 → avol[m] = avol0[m] ⊦ avol[(n + m) + n1] = avol0[(n + m) + n1]

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: (n + m) + n1

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ m + n < m; (s) Used terms: (n + m) + n1