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Proof step 29 from proof perm-shift-two (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ bag -- a -- b = bag -- b -- a
Proof step 31:
(mkbag(A, # A) -- A[m + 1] -- A[m + 2]) ++ A[m + 1] ++ b = mkbag(A0, # A0), m + 1 < # A, m + 2 < # A, m < # A ⊦ (mkbag(A, # A) -- A[m + 2] -- A[m]) ++ A[m] = (mkbag(A, # A) -- A[m + 1] -- A[m + 2]) ++ A[m + 1], A[m + 1] = A[m + 2], b = A[m + 2]

Rule argument

spec: <toplevel> name: bag-swap-del seq: ⊦ bag -- a -- b = bag -- b -- a subst: [b, a, bag] → [A[m + 2], A[m], mkbag(A, # A)] flags: <all paths>

Additional information

Used terms: A[m + 2], A[m], mkbag(A, # A)