Expression of type InSet

from the theory of proveit.physics.quantum.QPE

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.linear_algebra import TensorProd
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, two
from proveit.physics.quantum.QPE import _Psi_ket, _ket_u, _s, _two_pow_t

# build up the expression from sub-expressions
expr = InSet(TensorProd(_Psi_ket, _ket_u), TensorProd(CartExp(Complex, _two_pow_t), CartExp(Complex, Exp(two, _s))))

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(\lvert \Psi \rangle {\otimes} \lvert u \rangle\right) \in \left(\mathbb{C}^{2^{t}} {\otimes} \mathbb{C}^{2^{s}}\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	Literal
10	Operation	operator: 13 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	16, 15
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 19 operands: 18
16	Literal
17	Operation	operator: 19 operands: 20
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22, 23
21	Literal
22	Literal
23	Literal