Theorem _success_complements_failure 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 _success_complements_failure

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

Passed sanity check: _success_complements_failure 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 success}\right]\left(e\right) = \left(1 - \left[P_{\rm fail}\right]\left(e\right)\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: 30 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	30, 13
11	Operation	operator: 14 operand: 30
12	Operation	operator: 33 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	39, 18
16	Literal
17	ExprTuple	39, 19
18	Operation	operator: 37 operand: 22
19	Operation	operator: 33 operands: 21
20	ExprTuple	22
21	ExprTuple	23, 24
22	Operation	operator: 25 operand: 30
23	Operation	operator: 27 operands: 28
24	Operation	operator: 37 operand: 32
25	Literal
26	ExprTuple	30
27	Literal
28	ExprTuple	32, 31
29	ExprTuple	32
30	Variable
31	Operation	operator: 33 operands: 34
32	Literal
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Operation	operator: 37 operand: 39
37	Literal
38	ExprTuple	39
39	Literal