Expression of type Equals

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 import Conditional, k, t
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, one, subtract, zero
from proveit.physics.quantum import NumKet, ket0
from proveit.physics.quantum.QPE import two_pow_t

# build up the expression from sub-expressions
sub_expr1 = TensorProd(ket0, NumKet(k, t))
expr = Equals(Conditional(sub_expr1, InSet(k, Interval(zero, subtract(two_pow_t, one)))), sub_expr1)

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 0 \rangle {\otimes} \lvert k \rangle_{t} \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right.. = \left(\lvert 0 \rangle {\otimes} \lvert k \rangle_{t}\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	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	19, 12
10	Operation	operator: 13 operand: 20
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	20
15	Literal
16	ExprTuple	19, 31
17	Literal
18	ExprTuple	20, 21
19	Variable
20	Literal
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operand: 32
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32
30	Literal
31	Variable
32	Literal