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 import Lambda, l
from proveit.logic import Bijections, InSet
from proveit.numbers import Add, Mod
from proveit.physics.quantum.QPE import _b_floor, _full_domain, _m_domain, _two_pow_t

# build up the expression from sub-expressions
expr = InSet(Lambda(l, Mod(Add(_b_floor, l), _two_pow_t)), Bijections(_full_domain, _m_domain))

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[l \mapsto \left(\left(b_{\textit{f}} + l\right) ~\textup{mod}~ 2^{t}\right)\right] \in \left[\{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} \xrightarrow[\text{onto}]{\text{1-to-1}} \{0~\ldotp \ldotp~2^{t} - 1\}\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	Lambda	parameter: 22 body: 6
4	Operation	operator: 7 operands: 8
5	ExprTuple	22
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 26
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 34 operands: 17
14	ExprTuple	18, 29
15	Literal
16	ExprTuple	19, 20
17	ExprTuple	21, 22
18	Operation	operator: 34 operands: 23
19	Literal
20	Operation	operator: 34 operands: 24
21	Literal
22	Variable
23	ExprTuple	25, 40
24	ExprTuple	26, 37
25	Operation	operator: 38 operand: 29
26	Operation	operator: 30 operands: 28
27	ExprTuple	29
28	ExprTuple	32, 36
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal