Theorem norm_is_nonneg of type Forall

from the theory of proveit.linear_algebra.inner_products

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.linear_algebra.inner_products import norm_is_nonneg

# check that the built expression is the same as the stored expression
assert norm_is_nonneg.expr == stored_expr
assert norm_is_nonneg.expr._style_id == stored_expr._style_id
print("Passed sanity check: norm_is_nonneg matches stored_expr")

Passed sanity check: norm_is_nonneg matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{K}~\left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(H\right)}~\left[\forall_{x \in H}~\left(\left \|x\right \| \in \mathbb{R}^{\ge 0}\right)\right]\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 11 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 5 body: 4
3	ExprTuple	5
4	Operation	operator: 11 operand: 7
5	Variable
6	ExprTuple	7
7	Lambda	parameter: 27 body: 8
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operand: 15
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	27, 16
15	Lambda	parameter: 30 body: 17
16	Operation	operator: 18 operand: 27
17	Conditional	value: 20 condition: 21
18	Literal
19	ExprTuple	27
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	30, 27
25	Operation	operator: 28 operand: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30
30	Variable