Theorem inner_prod_pos_def 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 inner_prod_pos_def

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

Passed sanity check: inner_prod_pos_def 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(K\right)}~\left[\forall_{x \in H~|~x \neq \vec{0}\left(H\right)}~\left(\left \langle x, x\right \rangle > 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: 9 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 21 body: 3
3	Operation	operator: 9 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 40 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	40, 14
13	Lambda	parameter: 36 body: 16
14	Operation	operator: 17 operand: 21
15	ExprTuple	36
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Variable
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	36, 36
32	Literal
33	ExprTuple	36, 40
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Variable