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, l
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, Neg, e, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [Abs(one), Abs(Neg(Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))))]), 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(\left|1\right|, \left|-\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}\right|\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: 12 operand: 15
9	Operation	operator: 12 operand: 16
10	ExprRange	lambda_map: 14 start_index: 15 end_index: 43
11	ExprTuple	15
12	Literal
13	ExprTuple	16
14	Lambda	parameter: 19 body: 19
15	Literal
16	Operation	operator: 34 operand: 20
17	ExprTuple	19
18	ExprTuple	20
19	Variable
20	Operation	operator: 39 operands: 21
21	ExprTuple	22, 23
22	Literal
23	Operation	operator: 32 operands: 24
24	ExprTuple	43, 25, 26, 27
25	Literal
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operand: 38
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operand: 45
38	Variable
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45
43	Literal
44	Literal
45	Literal