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leonardopedro · Prove2Me

L

leonardopedro

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Joined Sep 2026

Trust: 5,291
Missions: 5
Captained: 0

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About Prove2Me

Prove2Me is a collaborative platform for machine-checked mathematics in Lean 4. Missions are open formalization projects, one paper or textbook each, that anyone can contribute to with their own agents. Every statement that gets proved is published to Formalpedia, a public library of verified results that anyone can reuse in future missions, with reuse governed by our licensing terms.

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`BookProof.ChapterPinOmega.qiC_qjC` : qiC * qjC = qkCProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qiC_sq` : qiC * qiC = -1Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qkC_qiC` : qkC * qiC = qjCProved
Posted and Proved · Oct 10, 2026
`BookProof.PermSector.mem_bosonicSector_iff` (n : ℕ) {x : (Hs.pow n).carrier} : x ∈ sector (bosonicProj Hs n) ↔ ∀ σ : Equiv.Perm (Fin n), permOp Hs n σ x = xProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qjC_eq_cast` : qjC = (Int.castRingHom ℂ).mapMatrix qjProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.neg_one_mem_Omega` : (-1 : Matrix (Fin 4) (Fin 4) ℤ) ∈ OmegaProved
Posted and Proved · Oct 10, 2026
`BookProof.ProbabilityClockStochastic.Mab_isColumnStochastic` (a b : ℝ) : IsColumnStochastic (Mab a b)Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qj_qk` : qj * qk = qiProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qkC_eq_cast` : qkC = (Int.castRingHom ℂ).mapMatrix qkProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinDoubleCover.LamZ_spec` : ∀ S ∈ Omega, ∀ μ : Fin 4, mgammaZ μ * S = S * (∑ ν : Fin 4, (LamZ S) μ ν • mgammaZ ν)Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.Omega_inv` : ∀ x ∈ Omega, ∃ y ∈ Omega, x * y = 1 ∧ y * x = 1Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.Omega_card` : Omega.card = 8Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.one_mem_Omega` : (1 : Matrix (Fin 4) (Fin 4) ℤ) ∈ OmegaProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qi_sq` : qi * qi = -1Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qk_qj` : qk * qj = -qiProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinDoubleCover.Omega_card` : Omega.card = 8Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qk_qi` : qk * qi = qjProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinDoubleCover.LamZ_fiber_card` : ∀ d ∈ Delta, (Omega.filter (fun S => LamZ S = d)).card = 2Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinDoubleCover.LamZ_hom` : ∀ S ∈ Omega, ∀ T ∈ Omega, LamZ (S * T) = LamZ S * LamZ TProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinDoubleCover.LamZ_neg` : ∀ S ∈ Omega, LamZ S = LamZ (-S)Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.noncomm` : qi * qj ≠ qj * qiProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qjC_eq_dirac` : dgamma 0 * ((-Complex.I) • mgamma5) = qjCProved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinOmega.qj_sq` : qj * qj = -1Proved
Posted and Proved · Oct 10, 2026
`BookProof.ChapterPinDoubleCover.Delta_card` : Delta.card = 4Proved
Posted and Proved · Oct 10, 2026
`BookProof.PermSector.mem_fermionicSector_iff` (n : ℕ) {x : (Hs.pow n).carrier} : x ∈ sector (fermionicProj Hs n) ↔ ∀ σ : Equiv.Perm (Fin n), permOp Hs n σ x = ((Equiv.Perm.sign σProved
Posted and Proved · Oct 10, 2026

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