Theorem _failure_upper_bound of type Forall

from the theory of proveit.physics.quantum.QPE

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.QPE import _failure_upper_bound

# check that the built expression is the same as the stored expression
assert _failure_upper_bound.expr == stored_expr
assert _failure_upper_bound.expr._style_id == stored_expr._style_id
print("Passed sanity check: _failure_upper_bound matches stored_expr")

Passed sanity check: _failure_upper_bound matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}}~\left(\left[P_{\rm fail}\right]\left(e\right) \leq \left(\frac{1}{2 \cdot e} + \frac{1}{4 \cdot e^{2}}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 42 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	42, 13
11	Operation	operator: 14 operand: 42
12	Operation	operator: 40 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	ExprTuple	42
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	48, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 40 operands: 25
22	ExprTuple	48, 26
23	Literal
24	ExprTuple	48, 27
25	ExprTuple	28, 29
26	Operation	operator: 31 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 38 operands: 33
29	Operation	operator: 46 operand: 43
30	ExprTuple	43, 42
31	Literal
32	ExprTuple	35, 36
33	ExprTuple	43, 37
34	ExprTuple	43
35	Literal
36	Operation	operator: 38 operands: 39
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44, 45
42	Variable
43	Literal
44	Literal
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Literal