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 e, l
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, Neg, one, subtract
from proveit.physics.quantum.QPE import _neg_domain, _two_pow__t_minus_one

# build up the expression from sub-expressions
expr = Equals(InSet(l, _neg_domain), InSet(l, Interval(Add(Neg(_two_pow__t_minus_one), one), subtract(Neg(e), one))))

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 \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right) = \left(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-e - 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	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	9, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 12 operands: 11
9	Variable
10	Operation	operator: 12 operands: 13
11	ExprTuple	15, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 36 operand: 20
15	Operation	operator: 32 operands: 18
16	Operation	operator: 32 operands: 19
17	ExprTuple	20
18	ExprTuple	21, 38
19	ExprTuple	22, 35
20	Operation	operator: 32 operands: 23
21	Operation	operator: 36 operand: 26
22	Operation	operator: 36 operand: 27
23	ExprTuple	27, 38
24	ExprTuple	26
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	Variable
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Literal