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Proof step 3 from proof size-fill-h (previous step)

∀ ar, a, m. # fill(ar, a, m, n0) = # ar ⊦ # fill(ar, a, m, n0 +1) = # ar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ ar, a, m. # fill(ar, a, m, n0) = # ar ⊦ # fill(ar, a, m, n0) = # ar

Rule argument

Additional information

Used simplifier rules: Fill-succ: ⊦ fill(ar, a, m, n + 1) = fill(ar, a, m, n)[m + n, a];%Size-put: ⊦ # ar[n, a] = # ar; from specification array%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%succ: ⊦ m +1 = m + 1; from specification nat-basic2