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Proof step 1 from proof mkbag-del-add-content (conclusion)

m < i, i ≤ # A ⊦ (mkbag(A, i) -- A[m]) ++ A[m] = mkbag(A, i)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: index-in-mkbag: m < # A, m < n ⊦ A[m] ∈ mkbag(A, n);%bag-del-add: a ∈ bag ⊦ (bag -- a) ++ a = bag;% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)