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, three, two
from proveit.physics.quantum.QPE import _eps, _n, _t

# build up the expression from sub-expressions
sub_expr1 = Exp(_eps, two)
sub_expr2 = frac(one, _eps)
sub_expr3 = subtract(Exp(two, subtract(_t, _n)), one)
expr = greater_eq(Add(one, Neg(frac(one, Mult(two, sub_expr3))), Neg(frac(one, Mult(four, Exp(sub_expr3, two))))), subtract(one, frac(Mult(sub_expr1, Add(three, sub_expr2)), Mult(sub_expr1, Exp(Add(two, sub_expr2), 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 - \frac{1}{2 \cdot \left(2^{t - n} - 1\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right) \geq \left(1 - \frac{\epsilon^{2} \cdot \left(3 + \frac{1}{\epsilon}\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\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: 54 operands: 5
4	Operation	operator: 54 operands: 6
5	ExprTuple	53, 7
6	ExprTuple	53, 8, 9
7	Operation	operator: 58 operand: 13
8	Operation	operator: 58 operand: 14
9	Operation	operator: 58 operand: 15
10	ExprTuple	13
11	ExprTuple	14
12	ExprTuple	15
13	Operation	operator: 45 operands: 16
14	Operation	operator: 45 operands: 17
15	Operation	operator: 45 operands: 18
16	ExprTuple	19, 20
17	ExprTuple	53, 21
18	ExprTuple	53, 22
19	Operation	operator: 26 operands: 23
20	Operation	operator: 26 operands: 24
21	Operation	operator: 26 operands: 25
22	Operation	operator: 26 operands: 27
23	ExprTuple	29, 28
24	ExprTuple	29, 30
25	ExprTuple	51, 39
26	Literal
27	ExprTuple	31, 32
28	Operation	operator: 54 operands: 33
29	Operation	operator: 47 operands: 34
30	Operation	operator: 47 operands: 35
31	Literal
32	Operation	operator: 47 operands: 36
33	ExprTuple	37, 42
34	ExprTuple	50, 51
35	ExprTuple	38, 51
36	ExprTuple	39, 51
37	Literal
38	Operation	operator: 54 operands: 40
39	Operation	operator: 54 operands: 41
40	ExprTuple	51, 42
41	ExprTuple	43, 44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 58 operand: 53
45	Literal
46	ExprTuple	53, 50
47	Literal
48	ExprTuple	51, 52
49	ExprTuple	53
50	Literal
51	Literal
52	Operation	operator: 54 operands: 55
53	Literal
54	Literal
55	ExprTuple	56, 57
56	Literal
57	Operation	operator: 58 operand: 60
58	Literal
59	ExprTuple	60
60	Literal