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Proof step 13 from proof ole-last (previous step)

x0 + a ' = a1 + y, ordered≤(x0 + a '), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ x0 + a ' = [], a1 < a0, b < a, ordered≤((a0 ' + x0) + a ' + b ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
x0 + a ' = a1 ' + y, ordered≤(a1 ' + y), ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a), a = a1 ∨ a ∈ y, a1 ∈ x0 ∨ a1 = a ⊦ a1 < a0, b < a, ordered≤((a0 ' + x0) + a ' + b ')

Rule argument

Additional information

Used simplifier rules: cons-02: ⊦ ordered≤(a ' + x) → ordered≤(x);%app-01: ⊦ ordered≤(x + y) → ordered≤(y);% ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + a ' ≠ []; (s)% ⊦ a + x = a ' + x; (s)