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Proof step 4 from proof cputput-reverse (previous step)

⊦ # ar[m, a][n, b] = # ar[n, b][m, a] ∧ (∀ n0. n0 < # ar[m, a][n, b] → ar[m, a][n, b][n0] = ar[n, b][m, a][n0]), m = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n0 < # ar ⊦ m = n, ar[m, a][n, b][n0] = ar[n, b][m, a][n0], # 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