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Proof step 2 from proof perm-shift-two (previous step)

m + 2 < # A, perm(A[m + 1, a][m + 2, b], A0) ⊦ perm(A[m, a][m + 1, b][m + 2, A[m]], A0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
(mkbag(A[m + 1, a], # A) -- A[m + 2]) ++ b = mkbag(A0, # A0), m + 2 < # A ⊦ (mkbag(A[m, a][m + 1, b], # A) -- A[m + 2]) ++ A[m] = (mkbag(A[m + 1, a], # A) -- A[m + 2]) ++ b

Rule argument

Additional information

Used simplifier rules: perm: ⊦ perm(A, A0) ↔ mkbag(A, # A) = mkbag(A0, # A0);%mkbag-update: m < # A ⊦ m < n → mkbag(A[m, a], n) = (mkbag(A, n) -- A[m]) ++ a;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m = m + n ↔ n = 0; (s)%m ≠ n ⊦ ar[m, a][n] = ar[n]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # ar[n, a] = # ar; (s)