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 = Neg(e)
sub_expr2 = Mult(frac(one, Exp(two, one)), _two_pow_t)
expr = Equals(Add(subtract(_two_pow__t_minus_one, two), Add(Neg(_two_pow__t_minus_one), one, sub_expr1)), Add(subtract(sub_expr2, two), Add(Neg(sub_expr2), 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(\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(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right) + 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: 32 operands: 5
4	Operation	operator: 32 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 32 operands: 11
8	Operation	operator: 32 operands: 12
9	Operation	operator: 32 operands: 13
10	Operation	operator: 32 operands: 14
11	ExprTuple	23, 16
12	ExprTuple	15, 45, 18
13	ExprTuple	24, 16
14	ExprTuple	17, 45, 18
15	Operation	operator: 40 operand: 23
16	Operation	operator: 40 operand: 44
17	Operation	operator: 40 operand: 24
18	Operation	operator: 40 operand: 25
19	ExprTuple	23
20	ExprTuple	44
21	ExprTuple	24
22	ExprTuple	25
23	Operation	operator: 42 operands: 26
24	Operation	operator: 27 operands: 28
25	Variable
26	ExprTuple	44, 29
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 42 operands: 36
32	Literal
33	ExprTuple	39, 37
34	Literal
35	ExprTuple	45, 38
36	ExprTuple	44, 39
37	Operation	operator: 40 operand: 45
38	Operation	operator: 42 operands: 43
39	Literal
40	Literal
41	ExprTuple	45
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Literal