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, Mult, Neg, four, frac, greater_eq, one, subtract, two
from proveit.physics.quantum.QPE import Pfail, _e_value

# build up the expression from sub-expressions
expr = greater_eq(subtract(one, Pfail(_e_value)), Add(one, Neg(frac(one, Mult(two, _e_value))), Neg(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(1 - \left[P_{\rm fail}\right]\left(2^{t - n} - 1\right)\right) \geq \left(1 - \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	reversed	('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: 39 operands: 5
4	Operation	operator: 39 operands: 6
5	ExprTuple	38, 7, 8
6	ExprTuple	38, 9
7	Operation	operator: 43 operand: 13
8	Operation	operator: 43 operand: 14
9	Operation	operator: 43 operand: 15
10	ExprTuple	13
11	ExprTuple	14
12	ExprTuple	15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operand: 29
16	ExprTuple	38, 21
17	Literal
18	ExprTuple	38, 22
19	Literal
20	ExprTuple	29
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	36, 29
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Operation	operator: 33 operands: 28
28	ExprTuple	29, 36
29	Operation	operator: 39 operands: 30
30	ExprTuple	31, 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 43 operand: 38
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	38
36	Literal
37	Operation	operator: 39 operands: 40
38	Literal
39	Literal
40	ExprTuple	41, 42
41	Literal
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Literal