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 ExprRange, Variable
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Mult, one, three
from proveit.physics.quantum.QPE import _s, _t

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = Add(_t, _s)
expr = Equals(Len(operands = [ExprRange(sub_expr1, ExprRange(sub_expr2, [sub_expr1, sub_expr2], one, sub_expr3), one, three)]), Mult(three, sub_expr3)).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} |\left(\left(1, 1\right), \left(1, 2\right), \ldots, \left(1, t + s\right), \left(2, 1\right), \left(2, 2\right), \ldots, \left(2, t + s\right), \ldots\ldots, \left(3, 1\right), \left(3, 2\right), \ldots, \left(3, t + s\right)\right)| \\  = \left(3 \cdot \left(t + s\right)\right) \end{array} \end{array}

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.	()	(1)	('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: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	11, 16
9	ExprRange	lambda_map: 10 start_index: 15 end_index: 11
10	Lambda	parameter: 21 body: 13
11	Literal
12	ExprTuple	21
13	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
14	Lambda	parameter: 22 body: 18
15	Literal
16	Operation	operator: 19 operands: 20
17	ExprTuple	22
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Variable
22	Variable
23	Literal
24	Literal