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Proof step 6 from proof subarray-avol-write (previous step)

# avol = main + m, n < m, n0 < m ⊦ avol[main + n, aleb][main + n0] = subarray(avol, main, m)[n, aleb][n0]

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: main + n0 = main + n

Additional information

Used simplifier rules: ⊦ m ≠ n → avol[n, aleb][m] = avol[m]; (s)%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # avol ⊦ avol[m, aleb][m] = aleb; (s)% ⊦ # subarray(avol, m, n) = n; (s) Used formulas: main + n0 = main + n