frb_implies_uhecr
plain-language theorem explainer
The declaration shows that the fast radio burst ledger condition directly entails the ultra-high-energy cosmic ray ledger condition. Astrophysicists working on transient high-energy sources would cite this link when unifying FRB and UHECR data under the Recognition phi-ladder. The proof is a one-line term that returns the input hypothesis, using the definitional identity between the two propositions.
Claim. If the fast radio burst ledger condition holds, then the ultra-high-energy cosmic ray ledger condition holds, where the former is defined to be identical to the latter and the latter is the proposition $0 < phi$.
background
The FRBStructure module sits inside the Astrophysics section of the Recognition Science monolith. It introduces frb_from_ledger as a Prop that is definitionally equal to uhecr_from_ledger. The upstream definition uhecr_from_ledger states that this Prop is simply the inequality $0 < phi$, where phi is the self-similar fixed point forced by the T6 step of the UnifiedForcingChain.
proof idea
The proof is a one-line term wrapper that returns the supplied hypothesis h. It relies on the definitional equality frb_from_ledger := uhecr_from_ledger established in the same module.
why it matters
This theorem supplies a minimal consistency link between the FRB and UHECR ledger inputs inside the Astrophysics module. It ensures that any structural assumption drawn from fast radio burst observations automatically satisfies the positivity requirement used for ultra-high-energy cosmic ray modeling. The declaration closes a small interface in the ledger construction without touching the core forcing chain or the RCL identity.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.