Theorem ortho_projectors_are_idempotent 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 ortho_projectors_are_idempotent

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

Passed sanity check: ortho_projectors_are_idempotent matches stored_expr

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

\forall_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{X~|~X \subseteq \mathcal{H}}~\left[\forall_{P~|~P = \textrm{OrthoProj}\left(\mathcal{H}, X\right)}~\left(P^{2} = P\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: 16 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 36 body: 4
3	ExprTuple	36
4	Conditional	value: 5 condition: 6
5	Operation	operator: 16 operand: 10
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	36, 11
10	Lambda	parameter: 37 body: 13
11	Literal
12	ExprTuple	37
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operand: 20
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	37, 36
20	Lambda	parameter: 34 body: 22
21	ExprTuple	34
22	Conditional	value: 23 condition: 24
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 34
26	Literal
27	ExprTuple	34, 29
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Variable
35	Literal
36	Variable
37	Variable