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, t
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Add, Neg, one, zero
from proveit.physics.quantum.QPE import _s

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [zero, ExprRange(sub_expr1, Add(sub_expr1, t), Add(Neg(t), one), zero), Add(t, _s)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, zero, Add(t, one))]))

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(0,\left(\left(-t + 1\right) + t\right), \left(\left(-t + 2\right) + t\right), \ldots, \left(0 + t\right), t + s\right)| = |\left(0, 1, \ldots, \left(t + 1\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	15, 8, 9
6	Literal
7	ExprTuple	10
8	ExprRange	lambda_map: 11 start_index: 12 end_index: 15
9	Operation	operator: 22 operands: 13
10	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
11	Lambda	parameter: 26 body: 17
12	Operation	operator: 22 operands: 18
13	ExprTuple	29, 19
14	Lambda	parameter: 26 body: 26
15	Literal
16	Operation	operator: 22 operands: 21
17	Operation	operator: 22 operands: 23
18	ExprTuple	24, 25
19	Literal
20	ExprTuple	26
21	ExprTuple	29, 25
22	Literal
23	ExprTuple	26, 29
24	Operation	operator: 27 operand: 29
25	Literal
26	Variable
27	Literal
28	ExprTuple	29
29	Variable