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 ExprRange, Variable
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, four, frac, one, two
from proveit.physics.quantum.QPE import _e_value

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Neg(frac(one, Mult(two, _e_value))), Neg(frac(one, Mult(four, Exp(_e_value, two))))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(-\frac{1}{2 \cdot \left(2^{t - n} - 1\right)}, -\frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right)| = |\left(1, \ldots, 2\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	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 43 operand: 14
9	Operation	operator: 43 operand: 15
10	ExprRange	lambda_map: 13 start_index: 38 end_index: 36
11	ExprTuple	14
12	ExprTuple	15
13	Lambda	parameter: 20 body: 20
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	20
17	ExprTuple	38, 21
18	Literal
19	ExprTuple	38, 22
20	Variable
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	36, 29
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 33 operands: 28
28	ExprTuple	29, 36
29	Operation	operator: 39 operands: 30
30	ExprTuple	31, 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 43 operand: 38
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	38
36	Literal
37	Operation	operator: 39 operands: 40
38	Literal
39	Literal
40	ExprTuple	41, 42
41	Literal
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Literal