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Theorem equal-same

⊦ 0 < j → (rational(i, j) = rational(i0, j) ↔ i = i0)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: add-eq, div-def-01, elim-sub, equality-def, int2rat-equal, one, root-is-irrational, totality,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas: numerator-pos, numerator-zero, denominator-pos, Equality,
Used spec theorems:
Used simplifier rules: