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plain-language theorem explainer
This definition supplies the constructor for closed intervals with rational endpoints. Numerics code in Recognition Science invokes it to create verified bounds for transcendental functions. The implementation is a direct structure literal that records the supplied bounds and the ordering hypothesis.
Claim. The constructor that forms a closed interval $[lo, hi]$ with $lo, hi$ rational and $lo ≤ hi$.
background
The module supplies verified interval arithmetic over the reals by using exact rational endpoints to bound real values. The Interval structure consists of rational lower and upper bounds together with a proof that the lower does not exceed the upper. This setup permits Lean to compute rigorous enclosures without floating-point error.
proof idea
The definition directly populates the three fields of the Interval structure: lower bound, upper bound, and the validity proof supplied by the caller or the default decide tactic.
why it matters
This constructor is the entry point for interval objects that feed into the construction of integers and rationals from logical primitives. It supports the numerics layer required for phi-ladder computations and J-cost evaluations. No open questions attach to this basic definition.
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