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The original `lt` compared raw cross-multiplied numerators directly (a*d < c*b), which is only correct when both denominators share the same sign. Since ZFInt' only requires nonzero (not positive) denominators, two representatives of the same rational can disagree in sign, making the old formula give different truth values for equivalent inputs (counterexample: 1/2 vs -1/-2 compared against 1/3). Redefine positivity via `isPos z := 0 < z.num * z.den`, well-defined by a squaring argument (multiply the cross-mult equation by den*den), and derive `lt x y := isPos (y - x)`, which is well-defined for free since it composes already-well-defined quotient operations. Add isPos_eq/lt_eq unfolding lemmas matching the file's existing _eq convention.
Build on the now-sound isPos/lt to establish: - isPos cone lemmas (trichotomy, closure under +/*, not both z and -z) - lt/le order facts (irrefl, asymm, trans, trichotomy, refl, antisymm, total) derived from the cone - LinearOrder ZFRat - IsOrderedRing, PosMulStrictMono, MulPosStrictMono ZFRat, mirroring the compositional mixin style already used for ZFInt's order instances rather than the older monolithic LinearOrderedRing
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