theorem
proved
term proof
add_comm
show as:
view Lean formalization →
formal statement (Lean)
36theorem add_comm (φ₁ φ₂ : ScalarField) :
37 ∀ x, eval (add φ₁ φ₂) x = eval (add φ₂ φ₁) x := by
proof body
Term-mode proof.
38 intro x
39 simp [eval, add]
40 ring
41
used by (40)
-
H_dAlembert -
sub_eq_add -
PhiInt -
PhiInt -
canonicalPhiRingObj -
costFamily_neg_param -
PhiRingObj -
galerkinNS_hasDerivAt_duhamelRemainder_mode -
unitSphereSurface_D3 -
Jcost_one_plus_eps_quadratic -
Jcost_small_strain_bound -
dAlembert_to_ODE_general -
dAlembert_to_ODE_general -
dAlembert_product -
dAlembert_to_ODE_general_theorem -
dAlembert_to_ODE_theorem -
dAlembert_to_ODE_theorem -
Jcost_one_plus_eps_quadratic -
Jcost_small_strain_bound -
Jcost_log_second_deriv_normalized -
neutralityScore_shift1_of_periodic8 -
add_comm -
add_right_cancel -
dalembert_deriv_ode -
defect_symmetric -
fromInt_toInt -
conservation_from_balance -
kernel_response_limit -
response_function_is_real_part -
n_of_r_mono_A_of_nonneg_p