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, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Exp(two, Neg(_t))
expr = Equals(Len(operands = [sub_expr2, Exp(Abs(subtract(_delta_b_floor, Mult(l, sub_expr2))), Neg(one))]), 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(2^{-t}, \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|^{-1}\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	33, 8
6	Literal
7	ExprTuple	9
8	Operation	operator: 34 operands: 10
9	ExprRange	lambda_map: 11 start_index: 20 end_index: 36
10	ExprTuple	12, 13
11	Lambda	parameter: 18 body: 18
12	Operation	operator: 15 operand: 19
13	Operation	operator: 38 operand: 20
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	ExprTuple	20
18	Variable
19	Operation	operator: 21 operands: 22
20	Literal
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 25 operand: 28
24	Operation	operator: 38 operand: 29
25	Literal
26	ExprTuple	28
27	ExprTuple	29
28	Literal
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal