Of Yukawa Terms NSum subset of subset
SuperSymmetry.SU5.ChargeSpectrum.ofYukawaTermsNSum_subset_of_subset
Project documentation
The charges of those terms which can be regenerated with up-to n insertions of singlets needed to regenerate the Yukawa terms. Equivalently, the sum of up-to n integers each corresponding to a charge of the Yukawa terms. -/ def ofYukawaTermsNSum (x : ChargeSpectrum ๐ฉ) : โ โ Multiset ๐ฉ | 0 => {0} | n + 1 => x.ofYukawaTermsNSum n + (x.ofYukawaTermsNSu...
Exact Lean statement
lemma ofYukawaTermsNSum_subset_of_subset [DecidableEq ๐ฉ] {x y : ChargeSpectrum ๐ฉ}
(h : x โ y) (n : โ) :
x.ofYukawaTermsNSum n โ y.ofYukawaTermsNSum nFormal artifact
Lean source
lemma ofYukawaTermsNSum_subset_of_subset [DecidableEq ๐ฉ] {x y : ChargeSpectrum ๐ฉ} (h : x โ y) (n : โ) : x.ofYukawaTermsNSum n โ y.ofYukawaTermsNSum n := by induction n with | zero => simp [ofYukawaTermsNSum] | succ n ih => simp [ofYukawaTermsNSum] refine Multiset.subset_iff.mpr ?_ intro z simp only [Multiset.mem_add, Multiset.mem_bind, Multiset.mem_map] intro hr rcases hr with hr | โจz1, hz1, z2, hz2, hsumโฉ ยท left exact ih hr right use z1 constructor ยท exact ih hz1 use z2 simp_all only [and_true] apply ofYukawaTerms_subset_of_subset h exact hz2- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/Yukawa.lean:114-135
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