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 Variable
from proveit.numbers import Add, Exp, Mult, Neg, four, frac, greater_eq, one, subtract, two
from proveit.physics.quantum.QPE import _eps, _n, _t

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