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, e
from proveit.logic import InSet
from proveit.numbers import Real
from proveit.physics.quantum.QPE import Pfail, _e_domain

# build up the expression from sub-expressions
expr = Conditional(InSet(Pfail(e), Real), InSet(e, _e_domain))

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[P_{\rm fail}\right]\left(e\right) \in \mathbb{R} \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\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	13, 8
6	Operation	operator: 9 operand: 13
7	Literal
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	29, 14
13	Variable
14	Operation	operator: 23 operands: 15
15	ExprTuple	16, 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 27 operand: 22
18	Literal
19	ExprTuple	22, 21
20	ExprTuple	22
21	Operation	operator: 23 operands: 24
22	Literal
23	Literal
24	ExprTuple	25, 26
25	Literal
26	Operation	operator: 27 operand: 29
27	Literal
28	ExprTuple	29
29	Literal