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Proof step 4 from proof prime-product (previous step)

primes(ints), max(ints) ≤ i, 4 ^ i < Π ints, ∀ i0, ints. i→n(i0) < i→n(i) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ ints = [], dups(ints)

User applied rule cut formula

And obtained the following new goals

Proof step 5:
primes(ints), max(ints) ≤ i, 4 ^ i < Π ints, ∀ i0, ints. i→n(i0) < i→n(i) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ i ≤ 2, ints = [], dups(ints)

Rule argument

fma: i ≤ 2

Additional information

Used simplifier rules: forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%primes-le-2: ⊦ primes(ints) ∧ ¬ dups(ints) ∧ ints ≠ [] → (max(ints) ≤ 2 ↔ ints = 2 '); from specification intlist%e: ⊦ i ' ≠ []; from specification list[intlista]%primes-one: ⊦ primes(i ') ↔ prime(i); from specification intlist%prime-two-01: ⊦ prime(2); from specification int-gcd%max-one: ⊦ max(i ') = i; from specification intlist%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%product-one: ⊦ Π i ' = i; from specification intlist%c: ⊦ ¬ dups(i '); from specification list-dup[intlista] Used formulas: i ≤ 2