Expression of type Conditional

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 Conditional, Variable, t
from proveit.logic import InSet
from proveit.numbers import Add, Interval, Natural, Neg, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(Add(sub_expr1, t), Natural), InSet(sub_expr1, Interval(Add(Neg(t), one), zero)))

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\{\left({_{-}a} + t\right) \in \mathbb{N} \textrm{ if } {_{-}a} \in \{-t + 1~\ldotp \ldotp~0\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	12, 8
6	Operation	operator: 15 operands: 9
7	Literal
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 21
10	Literal
11	ExprTuple	13, 14
12	Variable
13	Operation	operator: 15 operands: 16
14	Literal
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 19 operand: 21
18	Literal
19	Literal
20	ExprTuple	21
21	Variable