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Proof step 3 from proof perm-shift-two (previous step)

(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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
(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, # A ≤ m + 1

Rule argument

fma: # A ≤ m + 1

Additional information

Used simplifier rules: mkbag-update-out-of-bound: ⊦ n ≤ m → mkbag(A[m, a], n) = mkbag(A, n);%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m + n < m + n0 ↔ n < n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: # A ≤ m + 1