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.logic import Equals
from proveit.numbers import Add, Exp, Neg, one, subtract, two
from proveit.physics.quantum.QPE import _t

# build up the expression from sub-expressions
sub_expr1 = Exp(two, subtract(_t, two))
sub_expr2 = subtract(sub_expr1, one)
expr = Equals(Add(sub_expr2, sub_expr2), Add(sub_expr1, Neg(one), sub_expr2)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left(\left(2^{t - 2} - 1\right) + \left(2^{t - 2} - 1\right)\right) =  \\ \left(2^{t - 2} - 1 + \left(2^{t - 2} - 1\right)\right) \end{array} \end{array}

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.	()	(2)	('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: 16 operands: 5
4	Operation	operator: 16 operands: 6
5	ExprTuple	7, 7
6	ExprTuple	9, 10, 7
7	Operation	operator: 16 operands: 8
8	ExprTuple	9, 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 20 operand: 15
11	Literal
12	ExprTuple	22, 14
13	ExprTuple	15
14	Operation	operator: 16 operands: 17
15	Literal
16	Literal
17	ExprTuple	18, 19
18	Literal
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Literal