refactor: Free simps
This commit is contained in:
jstoobysmith
parent
e5c85ac109
commit
22636db606
9 changed files with 205 additions and 171 deletions
|
|
@ -106,7 +106,7 @@ lemma ι_superCommute_zero_of_fermionic (φ ψ : 𝓕.CrAnStates)
|
|||
ι [ofCrAnState φ, ofCrAnState ψ]ₛca = 0 := by
|
||||
rw [← ofCrAnList_singleton, ← ofCrAnList_singleton] at h ⊢
|
||||
rcases statistic_neq_of_superCommute_fermionic h with h | h
|
||||
· simp [ofCrAnList_singleton]
|
||||
· simp only [ofCrAnList_singleton]
|
||||
apply ι_superCommute_of_diff_statistic
|
||||
simpa using h
|
||||
· simp [h]
|
||||
|
|
@ -116,7 +116,7 @@ lemma ι_superCommute_ofCrAnState_ofCrAnState_bosonic_or_zero (φ ψ : 𝓕.CrAn
|
|||
ι [ofCrAnState φ, ofCrAnState ψ]ₛca = 0 := by
|
||||
rcases superCommute_ofCrAnList_ofCrAnList_bosonic_or_fermionic [φ] [ψ] with h | h
|
||||
· simp_all [ofCrAnList_singleton]
|
||||
· simp_all [ofCrAnList_singleton]
|
||||
· simp_all only [ofCrAnList_singleton]
|
||||
right
|
||||
exact ι_superCommute_zero_of_fermionic _ _ h
|
||||
|
||||
|
|
@ -187,7 +187,7 @@ lemma ι_superCommute_ofCrAnState_ofCrAnState_mem_center (φ ψ : 𝓕.CrAnState
|
|||
have h0 := ι_commute_crAnAlgebra_superCommute_ofCrAnState_ofCrAnState φ ψ a
|
||||
trans ι ((superCommute (ofCrAnState φ)) (ofCrAnState ψ)) * ι a + 0
|
||||
swap
|
||||
simp
|
||||
simp only [add_zero]
|
||||
rw [← h0]
|
||||
abel
|
||||
|
||||
|
|
@ -208,7 +208,7 @@ lemma ι_eq_zero_iff_mem_ideal (x : CrAnAlgebra 𝓕) :
|
|||
lemma bosonicProj_mem_fieldOpIdealSet_or_zero (x : CrAnAlgebra 𝓕) (hx : x ∈ 𝓕.fieldOpIdealSet) :
|
||||
x.bosonicProj.1 ∈ 𝓕.fieldOpIdealSet ∨ x.bosonicProj = 0 := by
|
||||
have hx' := hx
|
||||
simp [fieldOpIdealSet] at hx
|
||||
simp only [fieldOpIdealSet, exists_prop, Set.mem_setOf_eq] at hx
|
||||
rcases hx with ⟨φ1, φ2, φ3, rfl⟩ | ⟨φc, φc', hφc, hφc', rfl⟩ | ⟨φa, φa', hφa, hφa', rfl⟩ |
|
||||
⟨φ, φ', hdiff, rfl⟩
|
||||
· rcases superCommute_superCommute_ofCrAnState_bosonic_or_fermionic φ1 φ2 φ3 with h | h
|
||||
|
|
@ -239,7 +239,7 @@ lemma bosonicProj_mem_fieldOpIdealSet_or_zero (x : CrAnAlgebra 𝓕) (hx : x ∈
|
|||
lemma fermionicProj_mem_fieldOpIdealSet_or_zero (x : CrAnAlgebra 𝓕) (hx : x ∈ 𝓕.fieldOpIdealSet) :
|
||||
x.fermionicProj.1 ∈ 𝓕.fieldOpIdealSet ∨ x.fermionicProj = 0 := by
|
||||
have hx' := hx
|
||||
simp [fieldOpIdealSet] at hx
|
||||
simp only [fieldOpIdealSet, exists_prop, Set.mem_setOf_eq] at hx
|
||||
rcases hx with ⟨φ1, φ2, φ3, rfl⟩ | ⟨φc, φc', hφc, hφc', rfl⟩ | ⟨φa, φa', hφa, hφa', rfl⟩ |
|
||||
⟨φ, φ', hdiff, rfl⟩
|
||||
· rcases superCommute_superCommute_ofCrAnState_bosonic_or_fermionic φ1 φ2 φ3 with h | h
|
||||
|
|
@ -275,11 +275,11 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
change p x hx
|
||||
apply AddSubgroup.closure_induction
|
||||
· intro x hx
|
||||
simp [p]
|
||||
simp only [p]
|
||||
obtain ⟨a, ha, b, hb, rfl⟩ := Set.mem_mul.mp hx
|
||||
obtain ⟨d, hd, y, hy, rfl⟩ := Set.mem_mul.mp ha
|
||||
rw [bosonicProj_mul, bosonicProj_mul, fermionicProj_mul]
|
||||
simp [mul_add, add_mul]
|
||||
simp only [add_mul]
|
||||
rcases fermionicProj_mem_fieldOpIdealSet_or_zero y hy with hfy | hfy
|
||||
<;> rcases bosonicProj_mem_fieldOpIdealSet_or_zero y hy with hby | hby
|
||||
· apply TwoSidedIdeal.add_mem
|
||||
|
|
@ -292,7 +292,7 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use bosonicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (bosonicProj y).1
|
||||
simp [hby]
|
||||
· use ↑(bosonicProj b)
|
||||
|
|
@ -305,7 +305,7 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use fermionicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (fermionicProj y).1
|
||||
simp [hby, hfy]
|
||||
· use ↑(bosonicProj b)
|
||||
|
|
@ -319,7 +319,7 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use bosonicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (fermionicProj y).1
|
||||
simp [hby, hfy]
|
||||
· use ↑(fermionicProj b)
|
||||
|
|
@ -332,12 +332,12 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use fermionicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (bosonicProj y).1
|
||||
simp [hby, hfy]
|
||||
· use ↑(fermionicProj b)
|
||||
simp
|
||||
· simp [hby]
|
||||
· simp only [hby, ZeroMemClass.coe_zero, mul_zero, zero_mul, zero_add, add_zero]
|
||||
apply TwoSidedIdeal.add_mem
|
||||
· /- fermion, fermion, boson mem-/
|
||||
rw [TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure]
|
||||
|
|
@ -347,7 +347,7 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use fermionicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (fermionicProj y).1
|
||||
simp [hby, hfy]
|
||||
· use ↑(bosonicProj b)
|
||||
|
|
@ -360,12 +360,12 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use bosonicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (fermionicProj y).1
|
||||
simp [hby, hfy]
|
||||
· use ↑(fermionicProj b)
|
||||
simp
|
||||
· simp [hfy]
|
||||
· simp only [hfy, ZeroMemClass.coe_zero, mul_zero, zero_mul, add_zero, zero_add]
|
||||
apply TwoSidedIdeal.add_mem
|
||||
· /- boson, boson, boson mem-/
|
||||
rw [TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure]
|
||||
|
|
@ -375,7 +375,7 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use bosonicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (bosonicProj y).1
|
||||
simp [hby]
|
||||
· use ↑(bosonicProj b)
|
||||
|
|
@ -388,7 +388,7 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
apply And.intro
|
||||
· apply Set.mem_mul.mpr
|
||||
use fermionicProj d
|
||||
simp
|
||||
simp only [Set.mem_univ, mul_eq_mul_left_iff, ZeroMemClass.coe_eq_zero, true_and]
|
||||
use (bosonicProj y).1
|
||||
simp [hby, hfy]
|
||||
· use ↑(fermionicProj b)
|
||||
|
|
@ -396,7 +396,7 @@ lemma bosonicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.spa
|
|||
· simp [hfy, hby]
|
||||
· simp [p]
|
||||
· intro x y hx hy hpx hpy
|
||||
simp_all [p]
|
||||
simp_all only [map_add, Submodule.coe_add, p]
|
||||
apply TwoSidedIdeal.add_mem
|
||||
exact hpx
|
||||
exact hpy
|
||||
|
|
@ -408,7 +408,7 @@ lemma fermionicProj_mem_ideal (x : CrAnAlgebra 𝓕) (hx : x ∈ TwoSidedIdeal.s
|
|||
have hb := bosonicProj_mem_ideal x hx
|
||||
rw [← ι_eq_zero_iff_mem_ideal] at hx hb ⊢
|
||||
rw [← bosonicProj_add_fermionicProj x] at hx
|
||||
simp at hx
|
||||
simp only [map_add] at hx
|
||||
simp_all
|
||||
|
||||
lemma ι_eq_zero_iff_ι_bosonicProj_fermonicProj_zero (x : CrAnAlgebra 𝓕) :
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue