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Proof step 7 from proof idexcept-extract-right (previous step)

# ar0 = # ar1, n0 < # ar1, ∀ m. m < # ar1 ∧ m ≠ n → ar0[m] = ar1[m] ⊦ # ar1 = 0, ar1[n0] = ar0[n, ar1[n]][n0]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 8:
# ar0 = # ar1, n0 < # ar1, ∀ m. m < # ar1 ∧ m ≠ n → ar0[m] = ar1[m] ⊦ n0 = n, # ar1 = 0, ar1[n0] = ar0[n, ar1[n]][n0]

Rule argument

fma: n0 = n

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%cgetput: m < # ar ⊦ ar[m, a][m] = a; from specification array Used formulas: n0 = n