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 Add, Exp, LessEq, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import Pfail, _e_domain

# build up the expression from sub-expressions
expr = Conditional(LessEq(Pfail(e), Add(frac(one, Mult(two, e)), frac(one, Mult(four, Exp(e, two))))), 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) \leq \left(\frac{1}{2 \cdot e} + \frac{1}{4 \cdot e^{2}}\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	38, 9
7	Operation	operator: 10 operand: 38
8	Operation	operator: 36 operands: 12
9	Operation	operator: 13 operands: 14
10	Literal
11	ExprTuple	38
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	44, 17
15	Operation	operator: 19 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 36 operands: 21
18	ExprTuple	44, 22
19	Literal
20	ExprTuple	44, 23
21	ExprTuple	24, 25
22	Operation	operator: 27 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 34 operands: 29
25	Operation	operator: 42 operand: 39
26	ExprTuple	39, 38
27	Literal
28	ExprTuple	31, 32
29	ExprTuple	39, 33
30	ExprTuple	39
31	Literal
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40, 41
38	Variable
39	Literal
40	Literal
41	Operation	operator: 42 operand: 44
42	Literal
43	ExprTuple	44
44	Literal