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
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Add(Neg(_two_pow__t_minus_one), one, Neg(e))
expr = Equals(Add(subtract(_two_pow__t_minus_one, two), sub_expr1), Add(subtract(Mult(frac(one, Exp(two, one)), _two_pow_t), two), 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(\left(2^{t - 1} - 2\right) + \left(-2^{t - 1} + 1 - e\right)\right) = \left(\left(\left(\frac{1}{2^{1}} \cdot 2^{t}\right) - 2\right) + \left(-2^{t - 1} + 1 - e\right)\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: 34 operands: 5
4	Operation	operator: 34 operands: 6
5	ExprTuple	7, 9
6	ExprTuple	8, 9
7	Operation	operator: 34 operands: 10
8	Operation	operator: 34 operands: 11
9	Operation	operator: 34 operands: 12
10	ExprTuple	24, 14
11	ExprTuple	13, 14
12	ExprTuple	15, 41, 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 39 operand: 36
15	Operation	operator: 39 operand: 24
16	Operation	operator: 39 operand: 25
17	Literal
18	ExprTuple	22, 23
19	ExprTuple	36
20	ExprTuple	24
21	ExprTuple	25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 32 operands: 28
24	Operation	operator: 32 operands: 29
25	Variable
26	Literal
27	ExprTuple	41, 30
28	ExprTuple	36, 37
29	ExprTuple	36, 31
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36, 41
34	Literal
35	ExprTuple	37, 38
36	Literal
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal