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Declaration
sqrt_sum_square_bound_from_ordered_args
Mathlib.Algebra.OrderedField.Basic
Packages
2
Module
63
Theorem
750
Declarations
1016
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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 (lt_rel : forall (a : Scalar), forall (b : Scalar), Prop), forall (sqrt_fn : forall (a : Scalar), Scalar), forall (ordered_args : @OrderedFieldLawArgs.{u} Scalar zero one add neg sub mul le_rel lt_rel sqrt_fn), forall (a : Scalar), forall (b : Scalar), forall (c : Scalar), forall (ha : le_rel zero a), forall (hb : le_rel zero b), forall (hc : le_rel zero c), forall (hsq : le_rel (@sq.{u} Scalar mul a) (@sq.{u} Scalar mul (add b c))), le_rel a (add b c)Proof term
fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun lt_rel => fun sqrt_fn => fun ordered_args => fun a => fun b => fun c => fun ha => fun hb => fun hc => fun hsq => @le_of_sq_le_sq_nonneg_from_ordered_args.{u} Scalar zero one add neg sub mul le_rel lt_rel sqrt_fn ordered_args a (add b c) ha (@add_dist_nonneg_from_ordered_args.{u} Scalar zero one add neg sub mul le_rel lt_rel sqrt_fn ordered_args b c hb hc) hsq