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Proof step 17 from proof count-mkbag-greater-one (previous step)

A[n] = A[m], count(A[m], mkbag(A, m)) = 0, n < m, n < # A, m < # A, n + 1 < # A, 2 ≤ # A ⊦ m = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
n < i, i ≤ # A, A[n] = a ⊦ count(a, mkbag(A, i)) ≠ 0

Rule argument

spec: <toplevel> name: count-mkbag-non-zero seq: n < i, i ≤ # A, A[n] = a ⊦ count(a, mkbag(A, i)) ≠ 0 subst: [n, i, A, a] → [n, m, A, A[m]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s) Used terms: n, m, A, A[m]