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Proof step 2 from proof ext-rec (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m < # ar0 ⊦ ar0[n, a][m] = (n = m ⊃ a;ar0[m]), # ar0 = 0

Rule argument

Additional information

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