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Proof step 1 from proof appins (conclusion)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 2:
perm(x, y), ordered≤(x), ordered≤(y) ⊦ x = y
Proof step 3:
⊦ 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))

Rule argument

spec: olist inst: name: eqdef seq: perm(x, y), ordered≤(x), ordered≤(y) ⊦ x = y subst: [x, y] → [sort(x + ins≤(a, y)), ins≤(a, sort(x + y))] flags:

Additional information

Used terms: sort(x + ins≤(a, y)), ins≤(a, sort(x + y))