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 Mult, frac, one
from proveit.physics.quantum.QPE import _b_round, _two_pow_t

# build up the expression from sub-expressions
expr = Equals(Mult(frac(Mult(one, _two_pow_t), one), frac(_b_round, Mult(_two_pow_t, one))), Mult(_two_pow_t, frac(_b_round, _two_pow_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())

\left(\frac{1 \cdot 2^{t}}{1} \cdot \frac{b_{\textit{r}}}{2^{t} \cdot 1}\right) = \left(2^{t} \cdot \frac{b_{\textit{r}}}{2^{t}}\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: 18 operands: 5
4	Operation	operator: 18 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	20, 9
7	Operation	operator: 12 operands: 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	14, 21
11	ExprTuple	16, 15
12	Literal
13	ExprTuple	16, 20
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	21, 20
18	Literal
19	ExprTuple	20, 21
20	Operation	operator: 22 operands: 23
21	Literal
22	Literal
23	ExprTuple	24, 25
24	Literal
25	Literal