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Proof step 27 from proof min-com (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
min(x3 + a0 ' + x) = min(x + x3), min(x + a ' + x3) = min((a ' + x3) + x), a < min((a ' + x3) + x), a0 < min((a ' + x3) + x), a < min(x + x3), min(x + x3) < min((a ' + x3) + x), ∀ x1, x2. #(x1 + x2) < #((a + x3) + (a0 + x)) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ x + x3 = [], a0 < min(x + x3)

Rule argument

Additional information

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