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Proof step 3 from proof primes-le-2 (previous step)

ints = i + ints0, primes(ints), max(ints) ≤ 2 ⊦ ints = [], ints = 2 ', dups(ints)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
max(ints0) ≤ 2, primes(ints0) ⊦ ints0 = [], 2 ∈ ints0, dups(ints0)

Rule argument

Additional information

Used simplifier rules: primes-rec: ⊦ primes(i ' + ints) ↔ prime(i) ∧ primes(ints);%max-le-rec: ⊦ 0 < j → (max(i ' + ints) ≤ j ↔ i ≤ j ∧ max(ints) ≤ j);%prime-two-01: ⊦ prime(2); from specification int-gcd%dups-cons: ⊦ dups(i ' + ints) ↔ dups(ints) ∨ i ∈ ints; from specification list-dup[intlista]%c-03: ⊦ i ' = i0 ' + ints ↔ i = i0 ∧ ints = []; from specification list[intlista]%prime-le-2: ⊦ prime(i) → (i ≤ 2 ↔ i = 2); from specification int-gcd%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%e-01: ⊦ i ' + ints ≠ []; from specification list[intlista]%c: ⊦ i + ints = i ' + ints; from specification list[intlista]