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

# build up the expression from sub-expressions
sub_expr1 = Mult(frac(one, Exp(two, one)), _two_pow_t)
expr = Equals(Add(subtract(sub_expr1, two), Add(Neg(sub_expr1), one, Neg(e))), subtract(Neg(one), e))

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(\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) = \left(-1 - e\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: 11 operands: 5
4	Operation	operator: 11 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 16
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 19 operand: 35
10	ExprTuple	21, 14
11	Literal
12	ExprTuple	15, 35, 16
13	ExprTuple	35
14	Operation	operator: 19 operand: 34
15	Operation	operator: 19 operand: 21
16	Operation	operator: 19 operand: 22
17	ExprTuple	34
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	Operation	operator: 23 operands: 24
22	Variable
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 32 operands: 29
27	Literal
28	ExprTuple	35, 30
29	ExprTuple	34, 31
30	Operation	operator: 32 operands: 33
31	Literal
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Literal