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.logic import Equals
from proveit.numbers import Add, Floor, Mult, Neg, frac, one, two
from proveit.physics.quantum.QPE import _delta_b_round, _phase, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(one, two)
sub_expr2 = Mult(_two_pow_t, _phase)
expr = Equals(Mult(_two_pow_t, _delta_b_round), Add(sub_expr2, sub_expr1, Neg(Floor(Add(sub_expr2, sub_expr1))), Neg(sub_expr1)))

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