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Proof step 43 from proof min-com (previous step)

min(x3 + a0 ' + x) = a0, min(x + a ' + x3) = min(x3 + x), a < min(x + x3), a0 < min(x + x3), a < a0, 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 = [], a = (a < min(x3 + x) ⊃ a;min(x3 + x)), a0 < min(x3 + x)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 44:
¬ a < min(x3 + x), min(x3 + a0 ' + x) = a0, min(x + a ' + x3) = min(x3 + x), a < min(x + x3), a0 < min(x + x3), a < a0, min(x3 + x) < min(x + x3), ∀ x1, x2. #(x1 + x2) < #((a + x3) + (a0 + x)) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ a = min(x3 + x), x3 + x = [], x + x3 = [], a0 < min(x3 + x)

Rule argument

pos: right 3

Proof step 43 from proof min-com (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

Additional information