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Proof step 8 from proof prime-def-prime (previous step)

0 < i, prime(j), j | i, 2 ≤ i, j * j ≤ i, 0 ≤ i, ∀ i0. 1 < i0 ∧ i0 < i → ¬ i0 | i ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: j abort: F discard: F computed: T

Additional information

Used simplifier rules: prime-one: ⊦ i ≤ 1 → ¬ prime(i);% ⊦ i < j ↔ ¬ j ≤ i; (ss)%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; (s)% ⊦ 0 < i → (i * j ≤ i ↔ j ≤ 1); (s)% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i = 1 → i * j = j; (s)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s) Used terms: j