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refactor(linear_algebra/*): Rename linear_equiv.range to linear_equiv.range_eq_top #18969

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2 changes: 1 addition & 1 deletion src/geometry/manifold/mfderiv.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1593,7 +1593,7 @@ lemma ker_mfderiv_eq_bot {x : M} (hx : x ∈ e.source) :

lemma range_mfderiv_eq_top {x : M} (hx : x ∈ e.source) :
linear_map.range (mfderiv I I' e x) = ⊤ :=
(he.mfderiv hx).to_linear_equiv.range
(he.mfderiv hx).to_linear_equiv.range_eq_top

lemma range_mfderiv_eq_univ {x : M} (hx : x ∈ e.source) :
range (mfderiv I I' e x) = univ :=
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4 changes: 2 additions & 2 deletions src/linear_algebra/basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1727,7 +1727,7 @@ include σ₂₁ re₁₂ re₂₁
rfl
omit σ₂₁ re₁₂ re₂₁

@[simp] protected theorem range : (e : M →ₛₗ[σ₁₂] M₂).range = ⊤ :=
@[simp] protected theorem range_eq_top : (e : M →ₛₗ[σ₁₂] M₂).range = ⊤ :=
linear_map.range_eq_top.2 e.to_equiv.surjective

include σ₂₁ re₁₂ re₂₁
Expand All @@ -1749,7 +1749,7 @@ linear_map.ker_eq_bot_of_injective e.to_equiv.injective
@[simp] theorem range_comp [ring_hom_surjective σ₁₂] [ring_hom_surjective σ₂₃]
[ring_hom_surjective σ₁₃] :
(h.comp (e : M →ₛₗ[σ₁₂] M₂) : M →ₛₗ[σ₁₃] M₃).range = h.range :=
linear_map.range_comp_of_range_eq_top _ e.range
linear_map.range_comp_of_range_eq_top _ e.range_eq_top

include module_M
@[simp] theorem ker_comp (l : M →ₛₗ[σ₁₂] M₂) :
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4 changes: 2 additions & 2 deletions src/linear_algebra/basis.lean
Original file line number Diff line number Diff line change
Expand Up @@ -157,7 +157,7 @@ by { rw ← b.coe_repr_symm, exact b.repr.apply_symm_apply v }
by { rw ← b.coe_repr_symm, exact b.repr.symm_apply_apply x }

lemma repr_range : (b.repr : M →ₗ[R] (ι →₀ R)).range = finsupp.supported R R univ :=
by rw [linear_equiv.range, finsupp.supported_univ]
by rw [linear_equiv.range_eq_top, finsupp.supported_univ]

lemma mem_span_repr_support {ι : Type*} (b : basis ι R M) (m : M) :
m ∈ span R (b '' (b.repr m).support) :=
Expand Down Expand Up @@ -541,7 +541,7 @@ b.constr_eq S $ λ x, rfl

lemma constr_range [nonempty ι] {f : ι → M'} :
(b.constr S f).range = span R (range f) :=
by rw [b.constr_def S f, linear_map.range_comp, linear_map.range_comp, linear_equiv.range,
by rw [b.constr_def S f, linear_map.range_comp, linear_map.range_comp, linear_equiv.range_eq_top,
← finsupp.supported_univ, finsupp.lmap_domain_supported, ←set.image_univ,
← finsupp.span_image_eq_map_total, set.image_id]

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2 changes: 1 addition & 1 deletion src/linear_algebra/dual.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1067,7 +1067,7 @@ begin
let f' := linear_map.quot_ker_equiv_of_surjective f hf,
transitivity linear_map.range (f.dual_map.comp f'.symm.dual_map.to_linear_map),
{ rw linear_map.range_comp_of_range_eq_top,
apply linear_equiv.range },
apply linear_equiv.range_eq_top },
{ apply congr_arg,
ext φ x,
simp only [linear_map.coe_comp, linear_equiv.coe_to_linear_map, linear_map.dual_map_apply,
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4 changes: 2 additions & 2 deletions src/linear_algebra/finsupp.lean
Original file line number Diff line number Diff line change
Expand Up @@ -933,8 +933,8 @@ variables {S}

@[simp]
lemma fintype.range_total : (fintype.total R S v).range = submodule.span R (set.range v) :=
by rw [← finsupp.total_eq_fintype_total, linear_map.range_comp,
linear_equiv.to_linear_map_eq_coe, linear_equiv.range, submodule.map_top, finsupp.range_total]
by rw [← finsupp.total_eq_fintype_total, linear_map.range_comp, linear_equiv.to_linear_map_eq_coe,
linear_equiv.range_eq_top, submodule.map_top, finsupp.range_total]

section span_range

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2 changes: 1 addition & 1 deletion src/linear_algebra/linear_independent.lean
Original file line number Diff line number Diff line change
Expand Up @@ -738,7 +738,7 @@ lemma linear_independent.repr_ker : hv.repr.ker = ⊥ :=
by rw [linear_independent.repr, linear_equiv.ker]

lemma linear_independent.repr_range : hv.repr.range = ⊤ :=
by rw [linear_independent.repr, linear_equiv.range]
by rw [linear_independent.repr, linear_equiv.range_eq_top]

lemma linear_independent.repr_eq
{l : ι →₀ R} {x} (eq : finsupp.total ι M R v l = ↑x) :
Expand Down