Expression of type And

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 A, B, n
from proveit.linear_algebra import Adj, MatrixSpace
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex

# build up the expression from sub-expressions
sub_expr1 = MatrixSpace(field = Complex, rows = n, columns = n)
expr = And(InSet(A, sub_expr1), InSet(B, sub_expr1), Equals(Adj(A), A), Equals(Adj(B), B))

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(A \in \mathbb{C}^{n \times n}\right) \land \left(B \in \mathbb{C}^{n \times n}\right) \land \left(A^{\dagger} = A\right) \land \left(B^{\dagger} = B\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',)

# 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, 5, 6
3	Operation	operator: 8 operands: 7
4	Operation	operator: 8 operands: 9
5	Operation	operator: 11 operands: 10
6	Operation	operator: 11 operands: 12
7	ExprTuple	23, 13
8	Literal
9	ExprTuple	24, 13
10	ExprTuple	14, 23
11	Literal
12	ExprTuple	15, 24
13	Operation	operator: 16 operands: 17
14	Operation	operator: 19 operand: 23
15	Operation	operator: 19 operand: 24
16	Literal
17	NamedExprs	field: 21 rows: 22 columns: 22
18	ExprTuple	23
19	Literal
20	ExprTuple	24
21	Literal
22	Variable
23	Variable
24	Variable