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Theorem div-def-01

⊦ 0 < j ∧ 0 < j0 ∧ i0 ≠ 0 → rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 21
Proof steps: 36
Used lemmas: div-neg, negate-eq, equality-def, zero-def, div-neg-01, negate-01, neg-intro, negate, equal-same, zero-num-02, denominator-zero, numerator-pos, numerator-zero, div-def, zero-num, zero-num-01, div-pos-def,
Used spec theorems:
- int-abs/abs-08
Used simplifier rules: