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Proof step 6 from proof perm-shift-one (previous step)

(mkbag(A, # A) -- A[m + 1]) ++ a = mkbag(A0, # A0), m + 1 < # A, m < # A ⊦ (mkbag(A, # A) -- A[m] -- A[m + 1]) ++ a ++ A[m] = (mkbag(A, # A) -- A[m + 1]) ++ a, a = A[m + 1]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
(mkbag(A, # A) -- A[m + 1]) ++ a = mkbag(A0, # A0), m < # A, m + 1 < # A ⊦ (mkbag(A, # A) -- A[m] -- A[m + 1]) ++ A[m] = mkbag(A, # A) -- A[m + 1], a = A[m + 1]

Rule argument

Additional information

Used simplifier rules: ⊦ bag0 ++ a ++ b = bag1 ++ a ↔ bag0 ++ b = bag1; (ss)