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Proof step 22 from proof ole-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
x0 + y.last ' = a1 ' + y, a0 < y.last, a1 < y.last, ordered≤(a1 ' + y), a1 ∈ x0, ∀ a, b. ordered≤(x0 + a ') → (ordered≤(x0 + a ' + b ') ↔ ¬ b < a) ⊦ a1 = y.last, y = [], b < a0, b < a1, a1 < a0, b < y.last, ordered≤((a0 ' + x0) + y.last ' + b ')

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ x → a ∈ x + y; (s)% ⊦ a ≠ b → (a ∈ b ' + x ↔ a ∈ x); (s)%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list% ⊦ a < b → (b < a ↔ false); (ss)% ⊦ x.last ∈ x ↔ x ≠ []; (s)%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%inapp-10: ⊦ a ' + x = y + b ' ∧ a ≠ b → a ∈ y ∧ b ∈ x; (forward) from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%lapp-04: ⊦ a ' + x = y + b ' ∧ a ≠ b → x.last = b; (forward) from specification list-last% ⊦ a ≠ b → (a < b ↔ ¬ b < a); (ss)