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Proof step 10 from proof eq (previous step)

a0 ' + ins≤(a, x0) = ins≤(a, y), a0 < a, a0 ∈ ins≤(a, y), ∀ a, y. ins≤(a, x0) = ins≤(a, y) → x0 = y ⊦ a0 ' + x0 = y

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ x ≠ [] ∧ x.first < a → ins≤(a, x) = x.first + ins≤(a, x.rest)
Proof step 12:
¬(y ≠ [] ∧ y.first < a), a0 ' + ins≤(a, x0) = ins≤(a, y), a0 < a, a0 ∈ ins≤(a, y), ∀ a, y. ins≤(a, x0) = ins≤(a, y) → x0 = y ⊦ a0 ' + x0 = y
Proof step 14:
y ≠ [] ∧ y.first < a, a0 ' + ins≤(a, x0) = y.first + ins≤(a, y.rest), a0 < a, a0 ∈ y.first + ins≤(a, y.rest), ∀ a, y. ins≤(a, x0) = ins≤(a, y) → x0 = y ⊦ a0 ' + x0 = y

Rule argument

spec: olist inst: name: ins-rec seq: ⊦ x ≠ [] ∧ x.first < a → ins≤(a, x) = x.first + ins≤(a, x.rest) subst: [x, a] → [y, a] flags: rewrite, current

Additional information

Used terms: y, a