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Proof step 5 from proof put-at-eq (previous step)

m ≠ 0, m ≤ # x0, ∀ m, a. m < # x0 → x0[m, a][m] = a ⊦ (a0 ' + x0[m -1, a])[m] = a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
m ≤ # x0, ∀ m, a. m < # x0 → x0[m, a][m] = a ⊦ m = 0, (a0 ' + x0[m - 1, a])[m] = a

Rule argument

Additional information

Used simplifier rules: pred-03: ⊦ n -1 = n - 1; from specification nat