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 l
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t

# build up the expression from sub-expressions
sub_expr1 = Exp(two, Neg(_t))
sub_expr2 = Mult(frac(one, two), sub_expr1, Exp(Abs(subtract(_delta_b_floor, Mult(l, sub_expr1))), Neg(one)))
expr = Equals(Mult(one, sub_expr2), sub_expr2)

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(1 \cdot \left(\frac{1}{2} \cdot 2^{-t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|^{-1}\right)\right) = \left(\frac{1}{2} \cdot 2^{-t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\right|^{-1}\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, 5
3	Operation	operator: 28 operands: 4
4	ExprTuple	18, 5
5	Operation	operator: 28 operands: 6
6	ExprTuple	7, 31, 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 32 operands: 11
9	Literal
10	ExprTuple	18, 34
11	ExprTuple	12, 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 36 operand: 18
14	Literal
15	ExprTuple	17
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	Literal
19	Literal
20	ExprTuple	21, 22
21	Operation	operator: 23 operand: 26
22	Operation	operator: 36 operand: 27
23	Literal
24	ExprTuple	26
25	ExprTuple	27
26	Literal
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Literal