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 Equals, InSet
from proveit.numbers import one, subtract
from proveit.physics.quantum.QPE import Pfail, Psuccess, _e_domain

# build up the expression from sub-expressions
expr = Conditional(Equals(Psuccess(e), subtract(one, Pfail(e))), 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 success}\right]\left(e\right) = \left(1 - \left[P_{\rm fail}\right]\left(e\right)\right) \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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	26, 9
7	Operation	operator: 10 operand: 26
8	Operation	operator: 29 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	35, 14
12	Literal
13	ExprTuple	35, 15
14	Operation	operator: 33 operand: 18
15	Operation	operator: 29 operands: 17
16	ExprTuple	18
17	ExprTuple	19, 20
18	Operation	operator: 21 operand: 26
19	Operation	operator: 23 operands: 24
20	Operation	operator: 33 operand: 28
21	Literal
22	ExprTuple	26
23	Literal
24	ExprTuple	28, 27
25	ExprTuple	28
26	Variable
27	Operation	operator: 29 operands: 30
28	Literal
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Operation	operator: 33 operand: 35
33	Literal
34	ExprTuple	35
35	Literal