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, m, n
from proveit.logic import And, InSet, NotEquals, TRUE
from proveit.physics.quantum.QPE import _m_domain

# build up the expression from sub-expressions
expr = Conditional(TRUE, And(InSet(m, _m_domain), InSet(n, _m_domain), NotEquals(m, n)))

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\{\top \textrm{ if } m \in \{0~\ldotp \ldotp~2^{t} - 1\} ,  n \in \{0~\ldotp \ldotp~2^{t} - 1\} ,  m \neq n\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	Literal
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6, 7
5	Operation	operator: 9 operands: 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	ExprTuple	14, 13
9	Literal
10	ExprTuple	15, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 16 operands: 17
14	Variable
15	Variable
16	Literal
17	ExprTuple	18, 19
18	Literal
19	Operation	operator: 20 operands: 21
20	Literal
21	ExprTuple	22, 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operand: 30
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30
28	Literal
29	Literal
30	Literal