Theorem cauchy_schwartz_inequality 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 cauchy_schwartz_inequality

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

Passed sanity check: cauchy_schwartz_inequality matches stored_expr

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

\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(\mathbb{C}\right)}~\left[\forall_{v, w \in H}~\left(\left \|\left \langle v, w\right \rangle\right \|^{2} \leq \left(\left \langle v, v\right \rangle \cdot \left \langle w, w\right \rangle\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 38 body: 4
3	ExprTuple	38
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	38, 12
11	Lambda	parameters: 45 body: 13
12	Operation	operator: 14 operand: 18
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 32 operands: 31
26	Operation	operator: 32 operands: 33
27	Literal
28	ExprTuple	34, 35
29	Literal
30	ExprTuple	36, 37
31	ExprTuple	46, 38
32	Literal
33	ExprTuple	47, 38
34	Operation	operator: 39 operand: 43
35	Literal
36	Operation	operator: 44 operands: 41
37	Operation	operator: 44 operands: 42
38	Variable
39	Literal
40	ExprTuple	43
41	ExprTuple	46, 46
42	ExprTuple	47, 47
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Variable