All proofs
Project-declaredLean 4.32.0 · mathlib@81a5d257c8e4

Mem minimally Allows Term Of Finset of minimally Allows Term

SuperSymmetry.SU5.ChargeSpectrum.mem_minimallyAllowsTermOfFinset_of_minimallyAllowsTerm

Project documentation

The multiset of all charges within ofFinset S5 S10 which minimally allow the potential term T. -/ def minimallyAllowsTermsOfFinset (S5 S10 : Finset 𝓩) : (T : PotentialTerm) → Multiset (ChargeSpectrum 𝓩) | μ => let SqHd := S5.val let SqHu := S5.val let prod := SqHd ×ˢ (SqHu) let Filt := prod.filter (fun x => - x.1 + x.2 = 0) (Filt.map (fun x => ⟨x.1,...

Exact Lean statement

lemma mem_minimallyAllowsTermOfFinset_of_minimallyAllowsTerm {S5 S10 : Finset 𝓩}
    {T : PotentialTerm} (x : ChargeSpectrum 𝓩) (h : x.MinimallyAllowsTerm T)
    (hx : x ∈ ofFinset S5 S10) :
    x ∈ minimallyAllowsTermsOfFinset S5 S10 T

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
lemma mem_minimallyAllowsTermOfFinset_of_minimallyAllowsTerm {S5 S10 : Finset 𝓩}    {T : PotentialTerm} (x : ChargeSpectrum 𝓩) (h : x.MinimallyAllowsTerm T)    (hx : x  ofFinset S5 S10) :    x  minimallyAllowsTermsOfFinset S5 S10 T := by  obtain a, b, c, rfl := eq_allowsTermForm_of_minimallyAllowsTerm h  cases T  all_goals    simp [allowsTermForm, minimallyAllowsTermsOfFinset]    rw [mem_ofFinset_iff] at hx  case μ =>    simp_all [allowsTermForm]  case β =>    exact {a}, by simp_all [allowsTermForm]  case Λ =>    exact {a, b}, {- a - b}, by simp_all [allowsTermForm]  case W1 =>    refine ⟨⟨{- a - b - c}, {a, b, c}, ?_, h    simp_all [allowsTermForm]    abel  case W2 =>    refine ⟨⟨{a, b, c}, ?_, h    simp_all [allowsTermForm]    abel  case W3 =>    use {b, - b - 2 • a}    simp_all [allowsTermForm]    abel  case W4 =>    exact {c}, by simp_all [allowsTermForm]  case K1 =>    exact {-a}, {b, - a - b}, by simp_all [allowsTermForm]  case K2 =>    exact {- a - b}, by simp_all [allowsTermForm]  case topYukawa =>    exact {b, - a - b}, by simp_all [allowsTermForm]  case bottomYukawa =>    exact {b}, {- a - b}, by simp_all [allowsTermForm]
Project
Physlib
License
Apache-2.0
Commit
dd43e9e65791
Source
Physlib/Particles/SuperSymmetry/SU5/ChargeSpectrum/MinimallyAllowsTerm/OfFinset.lean:470-506

Reuse this declaration

Bring the exact result into your workflow

The import identifies the source module. Your project still needs the pinned package dependency shown on this page.

What this badge means

This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.

Continue in this project

Related declarations

Project-declaredLean 4.32.0

Adiabatic relation log

adiabatic_relation_log

Plain-language statement

Adiabatic relation in logarithmic form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then c * log (Ua/Ub) + log (Va/Vb) = 0.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record
Project-declaredLean 4.32.0

Adiabatic relation Ua Ub Va Vb

adiabatic_relation_UaUbVaVb

Plain-language statement

Adiabatic relation in product form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then (Ua/Ub)^c * (Va/Vb) = 1.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record