Expression of type Len

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 And, Equals
from proveit.numbers import Add, Neg, one, two, zero
from proveit.physics.quantum.QPE import _s

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, _s)
expr = Len(operands = [Equals(zero, zero), Equals(one, Add(zero, one)), And(ExprRange(sub_expr1, Equals(Add(sub_expr1, t), Add(Add(sub_expr1, Neg(one), t), one)), Add(Neg(t), two), zero)), Equals(sub_expr2, 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(0 = 0, 1 = \left(0 + 1\right), \left(\left(\left(-t + 2\right) + t\right) = \left(\left(\left(-t + 2\right) - 1 + t\right) + 1\right)\right) \land  \left(\left(\left(-t + 3\right) + t\right) = \left(\left(\left(-t + 3\right) - 1 + t\right) + 1\right)\right) \land  \ldots \land  \left(\left(0 + t\right) = \left(\left(0 - 1 + t\right) + 1\right)\right), \left(t + s\right) = \left(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',)

# 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, 5, 6
3	Operation	operator: 24 operands: 7
4	Operation	operator: 24 operands: 8
5	Operation	operator: 9 operands: 10
6	Operation	operator: 24 operands: 11
7	ExprTuple	19, 19
8	ExprTuple	41, 12
9	Literal
10	ExprTuple	13
11	ExprTuple	14, 14
12	Operation	operator: 34 operands: 15
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 19
14	Operation	operator: 34 operands: 18
15	ExprTuple	19, 41
16	Lambda	parameter: 36 body: 21
17	Operation	operator: 34 operands: 22
18	ExprTuple	38, 23
19	Literal
20	ExprTuple	36
21	Operation	operator: 24 operands: 25
22	ExprTuple	26, 27
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 39 operand: 38
27	Literal
28	Operation	operator: 34 operands: 31
29	Operation	operator: 34 operands: 32
30	ExprTuple	38
31	ExprTuple	36, 38
32	ExprTuple	33, 41
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37, 38
36	Variable
37	Operation	operator: 39 operand: 41
38	Variable
39	Literal
40	ExprTuple	41
41	Literal