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, one
from proveit.physics.quantum.QPE import _s, _t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(_t, _s)
expr = Equals(sub_expr2, Len(operands = [ExprRange(sub_expr1, [Variable("_b", latex_format = r"{_{-}b}"), sub_expr1], one, 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(t + s\right) = |\left(\left({_{-}b}, 1\right), \left({_{-}b}, 2\right), \ldots, \left({_{-}b}, t + s\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	9, 3
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6
6	ExprRange	lambda_map: 7 start_index: 8 end_index: 9
7	Lambda	parameter: 15 body: 11
8	Literal
9	Operation	operator: 12 operands: 13
10	ExprTuple	15
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Variable
15	Variable
16	Literal
17	Literal