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Proof step 87 from proof min-com (previous step)

x3 + x ≠ [], min(x + a ' + x3) = (a < min(x3 + x) ⊃ a;min(x3 + x)), min(x3 + a0 ' + x) = a0, a0 < min(x + x3), (a < min(x3 + x) ⊃ a;min(x3 + x)) < a0, (a < min(x3 + x) ⊃ a;min(x3 + x)) < min(x + x3), ∀ x1, x2. #(x1 + x2) < #((a + x3) + (a0 + x)) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ a0 = (a < min(x3 + x) ⊃ a;min(x3 + x)), x + x3 = [], a < a0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
min(x3 + a0 ' + x) = a0, min(x + a ' + x3) = min(x3 + x), (a < min(x3 + x) ⊃ a;min(x3 + x)) < a0, a0 < min(x + x3), min(x3 + x) < min(x + x3), ∀ x1, x2. #(x1 + x2) < #((a + x3) + (a0 + x)) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ x3 + x = [], x + x3 = [], a0 = min(x3 + x), a < a0

Rule argument

Additional information

Used simplifier rules: nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%irreflexivity: ⊦ ¬ a < a; from specification oelem%lel: ⊦ a < b ∧ a = c → c < b; (forward) from specification oelem%sls: ⊦ a ≠ b → (¬ a < b ↔ b < a); from specification oelem%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem