[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 89 from proof Extsimple (previous step)

abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2), j1 / gcd(i1, j1) = abs(j2) / gcd(i2, j2), 0 < j1, 0 < i1 ∧ (0 < i2 ∧ 0 < j2 ∨ i2 < 0 ∧ j2 < 0) ∨ i1 < 0 ∧ (0 < i2 ∧ j2 < 0 ∨ i2 < 0 ∧ 0 < j2) ⊦ j2 = 0, j1 = 0, i2 = 0, i1 / gcd(i1, j1) = rational(i2, j2).num, i1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 90:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 91:
¬(i2 ≠ 0 ∧ 0 < j2), abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2), j1 / gcd(i1, j1) = abs(j2) / gcd(i2, j2), 0 < j1, 0 < i1 ∧ (0 < i2 ∧ 0 < j2 ∨ i2 < 0 ∧ j2 < 0) ∨ i1 < 0 ∧ (0 < i2 ∧ j2 < 0 ∨ i2 < 0 ∧ 0 < j2) ⊦ j2 = 0, j1 = 0, i2 = 0, i1 / gcd(i1, j1) = rational(i2, j2).num, i1 = 0
Proof step 94:
i2 ≠ 0 ∧ 0 < j2, abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2), j1 / gcd(i1, j1) = abs(j2) / gcd(i2, j2), 0 < j1, 0 < i1 ∧ (0 < i2 ∧ 0 < j2 ∨ i2 < 0 ∧ j2 < 0) ∨ i1 < 0 ∧ (0 < i2 ∧ j2 < 0 ∨ i2 < 0 ∧ 0 < j2) ⊦ j2 = 0, j1 = 0, i2 = 0, i1 / gcd(i1, j1) = i2 / gcd(i2, j2), i1 = 0

Rule argument

name: numerator-pos rotate: F subst: [j, i] → [j2, i2]

Additional information

Used terms: j2, i2