Skip to content
Merged
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
6 changes: 3 additions & 3 deletions Physlib/ClassicalMechanics/HarmonicOscillator/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -747,11 +747,11 @@ lemma equationOfMotion_tfae (xₜ : Time → EuclideanSpace ℝ (Fin 1)) (hx : C
∫ t, ⟪(pq' t).1, ∂ₜ (Prod.snd ∘ pq') t⟫_ℝ - S.hamiltonian t (pq' t).1 (pq' t).2) = 0] := by
rw [← equationOfMotion_iff_hamiltonEqOp_eq_zero, ← equationOfMotion_iff_newtons_2nd_law]
rw [hamiltons_equations_varGradient, euler_lagrange_varGradient]
simp only [List.tfae_cons_self]
simp only [List.tfae_cons_of_mem, List.mem_cons_self]
rw [← gradLagrangian_eq_eulerLagrangeOp, ← equationOfMotion_iff_gradLagrangian_zero]
simp only [List.tfae_cons_self]
simp only [List.tfae_cons_of_mem, List.mem_cons_self]
erw [← equationOfMotion_iff_hamiltonEqOp_eq_zero]
simp only [List.tfae_cons_self, List.tfae_singleton]
simp only [List.tfae_cons_of_mem, List.mem_cons_self, List.tfae_singleton]
repeat fun_prop
simp [toCanonicalMomentum_eq]
repeat fun_prop
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -309,14 +309,14 @@ lemma equationOfMotion_tfae (θ : Time → EuclideanSpace ℝ (Fin 1)) (hθ : Co
rw [← S.equationOfMotion_iff_hamiltonEqOp_eq_zero θ hθ,
← S.equationOfMotion_iff_scalar θ]
rw [hamiltons_equations_varGradient, euler_lagrange_varGradient]
simp only [List.tfae_cons_self]
simp only [List.tfae_cons_of_mem, List.mem_cons_self]
rw [← S.gradLagrangian_eq_eulerLagrangeOp θ hθ,
← S.equationOfMotion_iff_gradLagrangian_zero θ hθ]
simp only [List.tfae_cons_self]
simp only [List.tfae_cons_of_mem, List.mem_cons_self]
show List.TFAE [S.EquationOfMotion θ,
S.hamiltonEqOp (fun t => S.canonicalMomentum t (θ t) (∂ₜ θ t)) θ = 0]
rw [← S.equationOfMotion_iff_hamiltonEqOp_eq_zero θ hθ]
simp only [List.tfae_cons_self, List.tfae_singleton]
simp only [List.tfae_cons_of_mem, List.mem_cons_self, List.tfae_singleton]
· exact hθ
· exact S.contDiff_lagrangian _
· simp only [S.canonicalMomentum_eq]; fun_prop
Expand Down
6 changes: 2 additions & 4 deletions Physlib/SpaceAndTime/Space/Derivatives/Curl.lean
Original file line number Diff line number Diff line change
Expand Up @@ -490,10 +490,8 @@ lemma eq_neg_curl_of_div_zero (f : Space → EuclideanSpace ℝ (Fin 3)) (hf : C
rw [fderiv_comp _ (by fun_prop) (by fun_prop), fderiv_comp _ (by fun_prop) (by fun_prop),
fderiv_fun_smul (by fun_prop) (by fun_prop)]
simp only [Function.comp_apply, ContinuousLinearMap.fderiv, fderiv_fun_const, Pi.zero_apply,
fderiv_fun_id, ContinuousLinearMap.coe_comp, _root_.add_apply,
FunLike.coe_smul, Pi.smul_apply, _root_.zero_apply, smul_zero,
ContinuousLinearMap.smulRight_apply, ContinuousLinearMap.coe_id', id_eq, one_smul, zero_add,
PiLp.proj_apply]
fderiv_fun_id, ContinuousLinearMap.coe_comp, smul_zero, ContinuousLinearMap.smulRight_apply,
ContinuousLinearMap.coe_id', id_eq, one_smul, zero_add, PiLp.proj_apply]
have hi (x : Space) (i : Fin 3) : ∫ (t : ℝ) in 0..1, (t * f (t • x) i * 2) -
t * (- fderiv ℝ f (t • x) (t • x)) i ∂(volume) = f x i := by
trans ∫ (t : ℝ) in 0..1, fderiv ℝ (fun t => t ^ 2 * f (t • x) i) t 1 ∂(volume)
Expand Down
2 changes: 1 addition & 1 deletion QuantumInfo/ForMathlib/Filter.lean
Original file line number Diff line number Diff line change
Expand Up @@ -51,7 +51,7 @@ theorem ENNReal.tendsto_toReal_iff_of_eventually_ne_top
(hx : x ≠ ∞) : Tendsto (fun n => (f n).toReal) fi (𝓝 x.toReal) ↔ Tendsto f fi (𝓝 x) := by
have he₁ : f =ᶠ[fi] (fun n ↦ (f n).toNNReal) := by
rw [EventuallyEq]
peel hf with h
filter_upwards [hf] with i h
simp [h]
have he₂ : (fun n ↦ (f n).toReal) = (fun n ↦ ((f n).toNNReal : ℝ≥0∞).toReal) :=
rfl
Expand Down
2 changes: 1 addition & 1 deletion QuantumInfo/ForMathlib/LimSupInf.lean
Original file line number Diff line number Diff line change
Expand Up @@ -186,7 +186,7 @@ lemma exists_liminf_zero_of_forall_liminf_le_with_UB (y : ℝ≥0) (f : ℝ≥0
· beta_reduce
rwa [Filter.liminf_congr]
have h := hg₁.eventually (gt_mem_nhds <| half_pos hz)
peel h with h
filter_upwards [h] with n h
rw [min_eq_left h.le]

/- (∀ x, x > 0 → liminf (n ↦ f x n) ≤ y) →
Expand Down
3 changes: 2 additions & 1 deletion QuantumInfo/ForMathlib/Matrix.lean
Original file line number Diff line number Diff line change
Expand Up @@ -722,7 +722,8 @@ theorem PosSemidef.rsmul {n : Type*} [Fintype n] {M : Matrix n n ℂ} (hM : M.Po
rw [Matrix.posSemidef_iff_dotProduct_mulVec] at hM ⊢
constructor
· exact hM.1.smul_real c
· peel hM.2
· intro x
have := hM.2 x
rw [smul_mulVec, dotProduct_smul]
positivity

Expand Down
Loading