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 Add, Neg, frac, subtract
from proveit.physics.quantum.QPE import _b_floor, _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = frac(_b_floor, _two_pow_t)
sub_expr2 = frac(l, _two_pow_t)
expr = Equals(Add(sub_expr1, _delta_b_floor, Neg(Add(sub_expr1, sub_expr2))), Add(sub_expr1, _delta_b_floor, subtract(Neg(sub_expr1), 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(\frac{b_{\textit{f}}}{2^{t}} + \delta_{b_{\textit{f}}} - \left(\frac{b_{\textit{f}}}{2^{t}} + \frac{l}{2^{t}}\right)\right) = \left(\frac{b_{\textit{f}}}{2^{t}} + \delta_{b_{\textit{f}}} + \left(-\frac{b_{\textit{f}}}{2^{t}} - \frac{l}{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: 17 operands: 5
4	Operation	operator: 17 operands: 6
5	ExprTuple	22, 8, 7
6	ExprTuple	22, 8, 9
7	Operation	operator: 20 operand: 14
8	Operation	operator: 11 operand: 27
9	Operation	operator: 17 operands: 13
10	ExprTuple	14
11	Literal
12	ExprTuple	27
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 20 operand: 22
16	Operation	operator: 20 operand: 23
17	Literal
18	ExprTuple	22, 23
19	ExprTuple	22
20	Literal
21	ExprTuple	23
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 29
25	Literal
26	ExprTuple	28, 29
27	Literal
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal