Expression of type LessEq

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

# build up the expression from sub-expressions
expr = LessEq(Pfail(_e_value), Add(frac(one, Mult(two, _e_value)), frac(one, Mult(four, Exp(_e_value, two)))))

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[P_{\rm fail}\right]\left(2^{t - n} - 1\right) \leq \left(\frac{1}{2 \cdot \left(2^{t - n} - 1\right)} + \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 21
4	Operation	operator: 31 operands: 7
5	Literal
6	ExprTuple	21
7	ExprTuple	8, 9
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	30, 13
11	Literal
12	ExprTuple	30, 14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	28, 21
16	Literal
17	ExprTuple	18, 19
18	Literal
19	Operation	operator: 25 operands: 20
20	ExprTuple	21, 28
21	Operation	operator: 31 operands: 22
22	ExprTuple	23, 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 35 operand: 30
25	Literal
26	ExprTuple	28, 29
27	ExprTuple	30
28	Literal
29	Operation	operator: 31 operands: 32
30	Literal
31	Literal
32	ExprTuple	33, 34
33	Literal
34	Operation	operator: 35 operand: 37
35	Literal
36	ExprTuple	37
37	Literal