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Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 2,569 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.

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Showing 1,159 to 1,164 of 2,569 results.

Project-declaredLean 4.32.0

Mem powerset sum of mem reduce to Fluxes Five

FTheory.SU5.FiveQuanta.mem_powerset_sum_of_mem_reduce_toFluxesFive

Project documentation

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Reduce eq self of of Charges nodup

FTheory.SU5.FiveQuanta.reduce_eq_self_of_ofCharges_nodup

Project documentation

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Reduce num Anti Chiral D of mem elems No Exotics

FTheory.SU5.FiveQuanta.reduce_numAntiChiralD_of_mem_elemsNoExotics

Project documentation

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Reduce num Anti Chiral L of mem elems No Exotics

FTheory.SU5.FiveQuanta.reduce_numAntiChiralL_of_mem_elemsNoExotics

Project documentation

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Reduce num Chiral D of mem elems No Exotics

FTheory.SU5.FiveQuanta.reduce_numChiralD_of_mem_elemsNoExotics

Project documentation

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Reduce num Chiral L of mem elems No Exotics

FTheory.SU5.FiveQuanta.reduce_numChiralL_of_mem_elemsNoExotics

Project documentation

The reduce of FiveQuanta is a new FiveQuanta with all the fluxes corresponding to the same charge (i.e. representation) added together. -/ def reduce (x : FiveQuanta 𝓩) : FiveQuanta 𝓩 := x.toCharges.dedup.map fun q5 => (q5, ((x.filter (fun f => f.1 = q5)).map (fun y => y.2)).sum) /-! ### B.1. The reduced FiveQuanta has no duplicate elements -/ l...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record