Theorem: SciLean.IsSmoothLinearMap.const_zero_rule (SciLean/Core/FunctionPropositions/IsSmoothLinearMap.lean)

State before:
K : Type u_1
inst✝⁷ : RCLike K
X : Type u_2
inst✝⁶ : Vec K X
Y : Type u_3
inst✝⁵ : Vec K Y
Z : Type ?u.3750
inst✝⁴ : Vec K Z
ι : Type ?u.3761
inst✝³ : IndexType ι
inst✝² : LawfulIndexType ι
inst✝¹ : DecidableEq ι
E : ι → Type ?u.3788
inst✝ : (i : ι) → Vec K (E i)
⊢ IsSmoothLinearMap K fun x => 0
Tactic:
constructor <;> first | fun_prop | apply IsLinearMap.isLinearMap_const_zero
State after:
no goals

State before:
case right
K : Type u_1
inst✝⁷ : RCLike K
X : Type u_2
inst✝⁶ : Vec K X
Y : Type u_3
inst✝⁵ : Vec K Y
Z : Type ?u.3750
inst✝⁴ : Vec K Z
ι : Type ?u.3761
inst✝³ : IndexType ι
inst✝² : LawfulIndexType ι
inst✝¹ : DecidableEq ι
E : ι → Type ?u.3788
inst✝ : (i : ι) → Vec K (E i)
⊢ CDifferentiable K fun x => 0
Tactic:
fun_prop
State after:
no goals