Expression of type Equals

from the theory of proveit.physics.quantum.algebra

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import X, i, n
from proveit.core_expr_types import x_i
from proveit.linear_algebra import Hspace, OrthoProj, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
expr = Equals(OrthoProj(Hspace, X), VecSum(index_or_indices = [i], summand = Qmult(Ket(x_i), Bra(x_i)), domain = Interval(one, n)))

expr:

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

Passed sanity check: expr matches stored_expr

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

\textrm{OrthoProj}\left(\mathcal{H}, X\right) = \left(\sum_{i=1}^{n} \left(\lvert x_{i} \rangle \thinspace \langle x_{i} \rvert\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operand: 11
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11
9	Variable
10	Variable
11	Lambda	parameter: 32 body: 12
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	32, 21
19	Operation	operator: 22 operand: 27
20	Operation	operator: 23 operand: 27
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	27
25	Literal
26	ExprTuple	28, 29
27	IndexedVar	variable: 30 index: 32
28	Literal
29	Variable
30	Variable
31	ExprTuple	32
32	Variable