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Proof step 1 from proof Inv-main-reduce (conclusion)

⊦ Inv-main(A, A0, i) → ( Inv-main(A1, A2, i0) ↔ # A ≠ 0 ∧ # A = # A0 ∧ i ≤ # A ∧ sorted(A, 0, i) ∧ perm(A, A0) → # A1 ≠ 0 ∧ # A1 = # A2 ∧ i0 ≤ # A1 ∧ sorted(A1, 0, i0) ∧ perm(A1, A2))

System applied rule normalize

And obtained the following new goals

Proof step 2:
Inv-main(A, A0, i) ⊦ Inv-main(A1, A2, i0) ↔ # A ≠ 0 ∧ # A = # A0 ∧ i ≤ # A ∧ sorted(A, 0, i) ∧ perm(A, A0) → # A1 ≠ 0 ∧ # A1 = # A2 ∧ i0 ≤ # A1 ∧ sorted(A1, 0, i0) ∧ perm(A1, A2)

Proof step 1 from proof Inv-main-reduce (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information