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Proof step 10 from proof perm-shift-two (previous step)

(a = A[m + 2] ⊃ mkbag(A, # A) -- A[m + 1];(mkbag(A, # A) -- A[m + 1] -- A[m + 2]) ++ a) ++ A[m + 2] = mkbag(A0, # A0), a = A[m + 1], m + 1 < # A, m + 2 < # A, m < # A ⊦ (mkbag(A, # A) -- A[m]) ++ A[m] = (a = A[m + 2] ⊃ mkbag(A, # A) -- A[m + 1];(mkbag(A, # A) -- A[m + 1] -- A[m + 2]) ++ a) ++ A[m + 2]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
(A[m + 1] = A[m + 2] ⊃ mkbag(A, # A) -- A[m + 1];(mkbag(A, # A) -- A[m + 1] -- A[m + 2]) ++ A[m + 1]) ++ A[m + 2] = mkbag(A0, # A0), m < # A, m + 2 < # A, m + 1 < # A ⊦ mkbag(A, # A) = (A[m + 1] = A[m + 2] ⊃ mkbag(A, # A) -- A[m + 1];(mkbag(A, # A) -- A[m + 1] -- A[m + 2]) ++ A[m + 1]) ++ A[m + 2]

Rule argument

Additional information

Used simplifier rules: mkbag-del-add-content: m < i, i ≤ # A ⊦ (mkbag(A, i) -- A[m]) ++ A[m] = mkbag(A, i);% ⊦ m ≤ m; (s)