def
definition
def or abbrev
reciprocal
show as:
view Lean formalization →
formal statement (Lean)
798noncomputable def reciprocal : JAut :=
proof body
Definition body.
799 ⟨posInv, by
800 constructor
801 · intro x y
802 apply Subtype.ext
803 simp [posMul, posInv, mul_comm]
804 · intro x
805 simpa [posInv] using (J_reciprocal x.1 x.2).symm⟩
806
807/-- Composition of `J`-automorphisms. -/
used by (40)
-
aestheticCost_zero_at_optimum -
canonicalRecognitionCostSystem_cost_one -
continuous_bijective_preserves_J_eq_id_or_inv -
CostMorphism -
eq_id_of_map_two_eq_two -
eq_id_or_reciprocal -
equivFinTwo -
equivZModTwo -
id -
J_at_one -
reciprocalAuto -
reciprocal_comp_reciprocal -
reciprocal_involution -
reciprocal_ne_id -
reciprocal_preserves_cost -
CanonicalCert -
cert -
tau0_pos -
alphaLock_numerical_bounds -
V_pos_off_vacuum -
aczel_kernel_ode -
PrimitiveCostHypotheses -
primitive_to_uniqueness_of_kernel -
dAlembert_cosh_solution_of_contDiff -
dAlembert_to_ODE_hypothesis_of_contDiff -
dAlembert_cosh_solution_aczel -
dAlembert_cosh_solution_of_log_curvature -
SatisfiesCompositionLaw -
dAlembert_cosh_solution_aczel -
Jcost_continuous_pos