English
A root-level statement about prod_map_equivL for continuous linear equivalences.
Русский
Корневое утверждение о prod_map_equivL для непрерывных линейных эквивалентностей.
LaTeX
$$$$\\text{prod\\_map\\_equivL} : (f : X \\to M_1 \\equiv_L M_2) \\to (g : X \\to M_3 \\equiv_L M_4) \\Rightarrow \\text{произведение}$$$$
Lean4
/-- Constructs a `SeminormedGroup` structure from a `GroupSeminormClass` on a `Group`. -/
-- See note [reducible non-instances]
@[to_additive /-- Constructs a `SeminormedAddGroup` structure from an `AddGroupSeminormClass` on an
`AddGroup`. -/
]
abbrev toSeminormedGroup [Group α] [GroupSeminormClass F α ℝ] (f : F) : SeminormedGroup α
where
norm := f
dist x y := f (x / y)
dist_eq _ _ := rfl
dist_self _ := by simp
dist_comm x y := by simp only [← map_inv_eq_map f (x / y), inv_div]
dist_triangle x y z := by simpa using map_mul_le_add f (x / y) (y / z)
