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Proof step 3 from proof mkbag-update-out-of-bound (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
n0 < m, ∀ m, A, a. n0 ≤ m → mkbag(A[m, a], n0) = mkbag(A, n0) ⊦ mkbag(A[m, a], n0) = mkbag(A, n0)

Rule argument

Additional information

Used simplifier rules: mkbag-rec: ⊦ mkbag(A, n + 1) = mkbag(A, n) ++ A[n];% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ bag0 ++ a = bag1 ++ a ↔ bag0 = bag1; (s)%m ≠ n ⊦ ar[m, a][n] = ar[n]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m +1 = m + 1; (s)