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

# build up the expression from sub-expressions
expr = LessEq(Pfail(e), Add(Mult(frac(one, two), frac(one, e)), Mult(frac(one, four), frac(one, Exp(e, 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(e\right) \leq \left(\left(\frac{1}{2} \cdot \frac{1}{e}\right) + \left(\frac{1}{4} \cdot \frac{1}{e^{2}}\right)\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: 28
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	28
7	Literal
8	ExprTuple	9, 10
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 21 operands: 18
15	Operation	operator: 21 operands: 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	24, 29
19	ExprTuple	24, 28
20	ExprTuple	24, 23
21	Literal
22	ExprTuple	24, 25
23	Literal
24	Literal
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Variable
29	Literal