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Proof step 8 from proof ext-rec (previous step)

# ar0 = # ar1, ∀ m. m < # ar1 → ar1[m] = (n = m ⊃ a;ar0[m]) ⊦ # ar1 = # ar0[n, a] ∧ (∀ n0. n0 < # ar1 → ar1[n0] = ar0[n, a][n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# ar0 = # ar1, n0 < # ar1, ∀ m. m < # ar1 → ar1[m] = (n = m ⊃ a;ar0[m]) ⊦ # ar1 = 0, ar1[n0] = ar0[n, a][n0]

Rule argument

Additional information

Used simplifier rules: Size-put: ⊦ # ar[n, a] = # ar;%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1