| import OAI.Combinatorics.PolynomialVacuum.Algebra.BasePolynomials |
| |
| namespace OAI |
|
|
| namespace PolynomialVacuumAlgebra |
| open MvPolynomial Classical |
| theorem baseThree_node_0 (x y : ℂ) : |
| baseThree x y (T*x) .zero .zero .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.zero) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
| all_goals vacuum_ring_finish |
|
|
| theorem baseThree_node_1 (x y : ℂ) : |
| baseThree x y (T*x) .zero .zero .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.plus) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_2 (x y : ℂ) : |
| baseThree x y (T*x) .zero .zero .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.minus) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_3 (x y : ℂ) : |
| baseThree x y (T*x) .zero .plus .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.zero) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_4 (x y : ℂ) : |
| baseThree x y (T*x) .zero .plus .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.plus) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_5 (x y : ℂ) : |
| baseThree x y (T*x) .zero .plus .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.minus) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
| all_goals vacuum_ring_finish |
|
|
| theorem baseThree_node_6 (x y : ℂ) : |
| baseThree x y (T*x) .zero .minus .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.zero) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_7 (x y : ℂ) : |
| baseThree x y (T*x) .zero .minus .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.plus) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
| all_goals vacuum_ring_finish |
|
|
| theorem baseThree_node_8 (x y : ℂ) : |
| baseThree x y (T*x) .zero .minus .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.minus) ab * cup (.zero,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_9 (x y : ℂ) : |
| baseThree x y (T*x) .plus .zero .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.zero) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_10 (x y : ℂ) : |
| baseThree x y (T*x) .plus .zero .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.plus) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_11 (x y : ℂ) : |
| baseThree x y (T*x) .plus .zero .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.minus) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
| all_goals vacuum_ring_finish |
|
|
| theorem baseThree_node_12 (x y : ℂ) : |
| baseThree x y (T*x) .plus .plus .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.zero) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_13 (x y : ℂ) : |
| baseThree x y (T*x) .plus .plus .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.plus) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_14 (x y : ℂ) : |
| baseThree x y (T*x) .plus .plus .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.minus) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_15 (x y : ℂ) : |
| baseThree x y (T*x) .plus .minus .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.zero) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
| all_goals vacuum_ring_finish |
|
|
| theorem baseThree_node_16 (x y : ℂ) : |
| baseThree x y (T*x) .plus .minus .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.plus) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_17 (x y : ℂ) : |
| baseThree x y (T*x) .plus .minus .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.minus) ab * cup (.plus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_18 (x y : ℂ) : |
| baseThree x y (T*x) .minus .zero .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.zero) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_19 (x y : ℂ) : |
| baseThree x y (T*x) .minus .zero .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.plus) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
| all_goals vacuum_ring_finish |
|
|
| theorem baseThree_node_20 (x y : ℂ) : |
| baseThree x y (T*x) .minus .zero .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.zero,.minus) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_21 (x y : ℂ) : |
| baseThree x y (T*x) .minus .plus .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.zero) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
| all_goals vacuum_ring_finish |
|
|
| theorem baseThree_node_22 (x y : ℂ) : |
| baseThree x y (T*x) .minus .plus .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.plus) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_23 (x y : ℂ) : |
| baseThree x y (T*x) .minus .plus .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.plus,.minus) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_24 (x y : ℂ) : |
| baseThree x y (T*x) .minus .minus .zero = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.zero) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_25 (x y : ℂ) : |
| baseThree x y (T*x) .minus .minus .plus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.plus) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node_26 (x y : ℂ) : |
| baseThree x y (T*x) .minus .minus .minus = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (.minus,.minus) ab * cup (.minus,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| norm_num [baseTwo,baseThree,baseThreeFactor,sum_pair,sum_spin, |
| exchangeNumerator_eq_table,exchangeTable,exchangeDenominator,cup,charge,zpow_neg, |
| q_five_inv,q_four_inv,T,t,zeta,inv_pow,q_inv] |
|
|
| theorem baseThree_node (x y : ℂ) (a b c : Spin) : |
| baseThree x y (T*x) a b c = |
| (1+T)*x*(∑ ab : Pair, exchangeNumerator (T*x) y (b,c) ab * cup (a,ab.1) * (if ab.2=Spin.zero then 1 else 0)) := by |
| cases a < |
| · exact baseThree_node_0 x y |
| · exact baseThree_node_1 x y |
| · exact baseThree_node_2 x y |
| · exact baseThree_node_3 x y |
| · exact baseThree_node_4 x y |
| · exact baseThree_node_5 x y |
| · exact baseThree_node_6 x y |
| · exact baseThree_node_7 x y |
| · exact baseThree_node_8 x y |
| · exact baseThree_node_9 x y |
| · exact baseThree_node_10 x y |
| · exact baseThree_node_11 x y |
| · exact baseThree_node_12 x y |
| · exact baseThree_node_13 x y |
| · exact baseThree_node_14 x y |
| · exact baseThree_node_15 x y |
| · exact baseThree_node_16 x y |
| · exact baseThree_node_17 x y |
| · exact baseThree_node_18 x y |
| · exact baseThree_node_19 x y |
| · exact baseThree_node_20 x y |
| · exact baseThree_node_21 x y |
| · exact baseThree_node_22 x y |
| · exact baseThree_node_23 x y |
| · exact baseThree_node_24 x y |
| · exact baseThree_node_25 x y |
| · exact baseThree_node_26 x y |
| end PolynomialVacuumAlgebra |
|
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| end OAI |
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