Theorem: mderiv_ne_zero_iff (Ray/AnalyticManifold/OneDimension.lean)

State before:
S : Type
inst✝⁵ : TopologicalSpace S
cs : ChartedSpace ℂ S
inst✝⁴ : AnalyticManifold I S
T : Type
inst✝³ : TopologicalSpace T
ct : ChartedSpace ℂ T
inst✝² : AnalyticManifold I T
U : Type
inst✝¹ : TopologicalSpace U
cu : ChartedSpace ℂ U
inst✝ : AnalyticManifold I U
z : S
w : T
f : TangentSpace I z →L[ℂ] TangentSpace I w
u : TangentSpace I z
⊢ f u ≠ 0 ↔ f ≠ 0 ∧ u ≠ 0
Tactic:
simp only [← not_or]
State after:
S : Type
inst✝⁵ : TopologicalSpace S
cs : ChartedSpace ℂ S
inst✝⁴ : AnalyticManifold I S
T : Type
inst✝³ : TopologicalSpace T
ct : ChartedSpace ℂ T
inst✝² : AnalyticManifold I T
U : Type
inst✝¹ : TopologicalSpace U
cu : ChartedSpace ℂ U
inst✝ : AnalyticManifold I U
z : S
w : T
f : TangentSpace I z →L[ℂ] TangentSpace I w
u : TangentSpace I z
⊢ f u ≠ 0 ↔ ¬(f = 0 ∨ u = 0)

State before:
S : Type
inst✝⁵ : TopologicalSpace S
cs : ChartedSpace ℂ S
inst✝⁴ : AnalyticManifold I S
T : Type
inst✝³ : TopologicalSpace T
ct : ChartedSpace ℂ T
inst✝² : AnalyticManifold I T
U : Type
inst✝¹ : TopologicalSpace U
cu : ChartedSpace ℂ U
inst✝ : AnalyticManifold I U
z : S
w : T
f : TangentSpace I z →L[ℂ] TangentSpace I w
u : TangentSpace I z
⊢ f u ≠ 0 ↔ ¬(f = 0 ∨ u = 0)
Tactic:
exact Iff.not (mderiv_eq_zero_iff _ _)
State after:
no goals