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Proof step 2 from proof mkbag-update-out-of-bound (previous step)

n ≤ m ⊦ mkbag(A[m, a], n) = mkbag(A, n)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
n0 +1 ≤ m, ∀ m, A, a. n0 ≤ m → mkbag(A[m, a], n0) = mkbag(A, n0) ⊦ mkbag(A[m, a], n0 +1) = mkbag(A, n0 +1)

Rule argument

indvar: n

Additional information

Used simplifier rules: mkbag-base: ⊦ mkbag(A, 0) = ∅;%nat freely generated by 0, +1;;