Expression of type And

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 import A, ExprRange, IndexedVar, Variable, m, n
from proveit.logic import And, CartExp, InSet
from proveit.numbers import Complex, Exp, one, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), CartExp(Complex, Exp(two, IndexedVar(n, sub_expr1)))), one, m))

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_{1} \in \mathbb{C}^{2^{n_{1}}}\right) \land  \left(A_{2} \in \mathbb{C}^{2^{n_{2}}}\right) \land  \ldots \land  \left(A_{m} \in \mathbb{C}^{2^{n_{m}}}\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
3	ExprRange	lambda_map: 4 start_index: 5 end_index: 6
4	Lambda	parameter: 23 body: 7
5	Literal
6	Variable
7	Operation	operator: 8 operands: 9
8	Literal
9	ExprTuple	10, 11
10	IndexedVar	variable: 12 index: 23
11	Operation	operator: 13 operands: 14
12	Variable
13	Literal
14	ExprTuple	15, 16
15	Literal
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 20
19	Literal
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable