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Declaration
add_sq_eq_zero_iff
Mathlib.Algebra.OrderedField.Square
Packages
2
Module
63
Theorems
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 (law : forall (a : Scalar), forall (b : Scalar), forall (R : Prop), forall (mk : forall (forward : forall (hsum : @Eq.{u} Scalar (add (@sq.{u} Scalar mul a) (@sq.{u} Scalar mul b)) zero), forall (S : Prop), forall (mk_pair : forall (haz : @Eq.{u} Scalar a zero), forall (hbz : @Eq.{u} Scalar b zero), S), S), forall (backward : forall (hpair : forall (S : Prop), forall (mk_pair : forall (haz : @Eq.{u} Scalar a zero), forall (hbz : @Eq.{u} Scalar b zero), S), S), @Eq.{u} Scalar (add (@sq.{u} Scalar mul a) (@sq.{u} Scalar mul b)) zero), R), R), forall (a : Scalar), forall (b : Scalar), forall (R : Prop), forall (mk : forall (forward : forall (hsum : @Eq.{u} Scalar (add (@sq.{u} Scalar mul a) (@sq.{u} Scalar mul b)) zero), forall (S : Prop), forall (mk_pair : forall (haz : @Eq.{u} Scalar a zero), forall (hbz : @Eq.{u} Scalar b zero), S), S), forall (backward : forall (hpair : forall (S : Prop), forall (mk_pair : forall (haz : @Eq.{u} Scalar a zero), forall (hbz : @Eq.{u} Scalar b zero), S), S), @Eq.{u} Scalar (add (@sq.{u} Scalar mul a) (@sq.{u} Scalar mul b)) zero), R), RProof 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 law => fun a => fun b => fun R => fun mk => law a b R mk