Expression of type Equals

from the theory of proveit.physics.quantum.circuits

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.core_expr_types.expr_arrays import A11_to_Akl_varray, B11_to_Bkl_varray
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Equals(A11_to_Akl_varray, B11_to_Bkl_varray)

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())

\left(\begin{array}{cccc} 
 A_{1, 1} & A_{2, 1} & \cdots & A_{k, 1} \\
A_{1, 2} & A_{2, 2} & \cdots & A_{k, 2} \\
\vdots & \vdots & \ddots & \vdots \\
A_{1, l} & A_{2, l} & \cdots & A_{k, l} \\
\end{array}
\right) = \left(\begin{array}{cccc} 
 B_{1, 1} & B_{2, 1} & \cdots & B_{k, 1} \\
B_{1, 2} & B_{2, 2} & \cdots & B_{k, 2} \\
\vdots & \vdots & \ddots & \vdots \\
B_{1, l} & B_{2, l} & \cdots & B_{k, l} \\
\end{array}
\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	ExprTuple	5
4	ExprTuple	6
5	ExprRange	lambda_map: 7 start_index: 17 end_index: 9
6	ExprRange	lambda_map: 8 start_index: 17 end_index: 9
7	Lambda	parameter: 25 body: 10
8	Lambda	parameter: 25 body: 12
9	Variable
10	ExprTuple	13
11	ExprTuple	25
12	ExprTuple	14
13	ExprRange	lambda_map: 15 start_index: 17 end_index: 18
14	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
15	Lambda	parameter: 26 body: 19
16	Lambda	parameter: 26 body: 21
17	Literal
18	Variable
19	IndexedVar	variable: 22 indices: 24
20	ExprTuple	26
21	IndexedVar	variable: 23 indices: 24
22	Variable
23	Variable
24	ExprTuple	25, 26
25	Variable
26	Variable