[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 12 from proof max_prime_divisor-nls-03 (previous step)

j < j * i0, j < i0, 0 < j * i0, prime(j), prime(i0), 2 ≤ j * i0, 0 ≤ j * i0, ∀ j0. j < j0 ∧ j0 < j * i0 ∧ prime(j0) → ¬ j0 | j * i0 ⊦ prime(j * i0)

User applied rule all left

And closed the goal!

Rule argument

pos: left 8 terms: i0 abort: F discard: T computed: T

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;%prime-one: ⊦ i ≤ 1 → ¬ prime(i);%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 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-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs% ⊦ 0 < i → (i * j ≤ i ↔ j ≤ 1); (s)% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s) Used terms: i0