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Proof step 3 from proof appins (previous step)

⊦ perm(sort(x + ins≤(a, y)), ins≤(a, sort(x + y))) ∧ ordered≤(sort(x + ins≤(a, y))) ∧ ordered≤(ins≤(a, sort(x + y))), sort(x + ins≤(a, y)) = ins≤(a, sort(x + y))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ sort(x + ins≤(a, y)) = ins≤(a, sort(x + y)), perm(x + ins≤(a, y), a ' + sort(x + y)), perm(x + ins≤(a, y), ins≤(a, sort(x + y))), perm(a ' + sort(x + y), x + ins≤(a, y))

Rule argument

Additional information

Used simplifier rules: perm: ⊦ perm(sort(x), y) ↔ perm(x, y);%Ordered: ⊦ ordered≤(sort(x));%c: ⊦ a + x = a ' + x; from specification list%insperm-03: ⊦ perm(ins≤(a, x), y) ↔ perm(a + x, y); from specification olist%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x); (forward) from specification list-perm%ole-01: ⊦ ordered≤(ins≤(a, x)) ↔ ordered≤(x); from specification olist