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Proof step 9 from proof mkbag-update (previous step)

A[n0] = A[m], mkbag(A[m, a], n0) = (mkbag(A, n0) -- A[m]) ++ a, m < # A, m ≤ n0, ∀ m, A, a. m < n0 ∧ m < # A → mkbag(A[m, a], n0) = (mkbag(A, n0) -- A[m]) ++ a ⊦ (mkbag(A, n0) -- A[m]) ++ A[m, a][n0] = mkbag(A, n0)

User applied rule all left

And obtained the following new goals

Proof step 10:
A[n0] = A[m], mkbag(A[m, a], n0) = (mkbag(A, n0) -- A[m]) ++ a, m < # A, m ≤ n0, m < n0 ∧ m < # A → mkbag(A[m, A[m, a][n0]], n0) = (mkbag(A, n0) -- A[m]) ++ A[m, a][n0], ∀ m, A, a. m < n0 ∧ m < # A → mkbag(A[m, a], n0) = (mkbag(A, n0) -- A[m]) ++ a ⊦ (mkbag(A, n0) -- A[m]) ++ A[m, a][n0] = mkbag(A, n0)

Rule argument

pos: left 5 terms: m, A, A[m, a][n0] abort: F discard: F computed: T

Additional information

Used terms: m, A, A[m, a][n0]