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Proof step 3 from proof cputput (previous step)

m < # ar ⊦ # ar[m, a][m, b] = # ar[m, b] ∧ (∀ n. n < # ar[m, a][m, b] → ar[m, a][m, b][n] = ar[m, b][n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
m < # ar, n < # ar ⊦ ar[m, a][m, b][n] = ar[m, b][n], # ar = 0

Rule argument

Additional information

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