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Declaration
LinearIsoArgs
Mathlib.Analysis.LinearMap
Packages
2
Module
63
Theorems
750
Declarations
1016
Untrusted sidecar
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Statement
forall (Scalar : Sort u), forall (zero : Scalar), forall (one : Scalar), forall (add : forall (a : Scalar), forall (b : Scalar), Scalar), forall (neg : forall (a : Scalar), Scalar), forall (sub : forall (a : Scalar), forall (b : Scalar), Scalar), forall (mul : forall (a : Scalar), forall (b : Scalar), Scalar), forall (le_rel : forall (a : Scalar), forall (b : Scalar), Prop), forall (X : Sort v), forall (xzero : X), forall (xadd : forall (x : X), forall (y : X), X), forall (xneg : forall (x : X), X), forall (xsmul : forall (a : Scalar), forall (x : X), X), forall (xnorm : forall (x : X), Scalar), forall (Y : Sort w), forall (yzero : Y), forall (yadd : forall (x : Y), forall (y : Y), Y), forall (yneg : forall (y : Y), Y), forall (ysmul : forall (a : Scalar), forall (y : Y), Y), forall (ynorm : forall (y : Y), Scalar), forall (f : forall (x : X), Y), forall (inv : forall (y : Y), X), forall (op_norm : Scalar), forall (inv_op_norm : Scalar), Prop
Proof term
fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun X => fun xzero => fun xadd => fun xneg => fun xsmul => fun xnorm => fun Y => fun yzero => fun yadd => fun yneg => fun ysmul => fun ynorm => fun f => fun inv => fun op_norm => fun inv_op_norm => forall (P : Prop), forall (mk : forall (forward_linear_law : @LinearMapLawArgs.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f), forall (inverse_linear_law : @LinearMapLawArgs.{u,w,v} Scalar zero one add neg sub mul le_rel Y yzero yadd yneg ysmul ynorm X xzero xadd xneg xsmul xnorm inv), forall (forward_bound_law : @OperatorNormBound.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f op_norm), forall (inverse_bound_law : @OperatorNormBound.{u,w,v} Scalar zero one add neg sub mul le_rel Y yzero yadd yneg ysmul ynorm X xzero xadd xneg xsmul xnorm inv inv_op_norm), forall (left_inverse_law : forall (x : X), @Eq.{v} X (inv (f x)) x), forall (right_inverse_law : forall (y : Y), @Eq.{w} Y (f (inv y)) y), P), P