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, _two_pow_t

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

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())

\frac{1}{2 \cdot 2^{t} \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|} = \frac{1}{2 \cdot 2^{t} \cdot \left|\delta_{b_{\textit{f}}} - \left(l \cdot 2^{-t}\right)\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: 32 operands: 5
4	Operation	operator: 32 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 34 operands: 10
8	Literal
9	Operation	operator: 34 operands: 11
10	ExprTuple	42, 36, 12
11	ExprTuple	42, 36, 13
12	Operation	operator: 15 operand: 17
13	Operation	operator: 15 operand: 18
14	ExprTuple	17
15	Literal
16	ExprTuple	18
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	23, 22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 44 operand: 29
23	Operation	operator: 26 operand: 30
24	Operation	operator: 44 operand: 31
25	ExprTuple	29
26	Literal
27	ExprTuple	30
28	ExprTuple	31
29	Operation	operator: 32 operands: 33
30	Literal
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	37, 36
34	Literal
35	ExprTuple	37, 38
36	Operation	operator: 40 operands: 39
37	Variable
38	Operation	operator: 40 operands: 41
39	ExprTuple	42, 46
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Operation	operator: 44 operand: 46
44	Literal
45	ExprTuple	46
46	Literal