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))))), Add(one, Neg(frac(one, Add(two, frac(one, _eps)))), Neg(frac(one, Mult(Variable("_a", latex_format = r"{_{-}a}"), Exp(Add(one, frac(one, Mult(two, _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 - \frac{1}{2 + \frac{1}{\epsilon}} - \frac{1}{{_{-}a} \cdot \left(1 + \frac{1}{2 \cdot \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: 56 operands: 5
4	Operation	operator: 56 operands: 6
5	ExprTuple	53, 7, 8
6	ExprTuple	53, 9, 10
7	Operation	operator: 62 operand: 15
8	Operation	operator: 62 operand: 16
9	Operation	operator: 62 operand: 17
10	Operation	operator: 62 operand: 18
11	ExprTuple	15
12	ExprTuple	16
13	ExprTuple	17
14	ExprTuple	18
15	Operation	operator: 46 operands: 19
16	Operation	operator: 46 operands: 20
17	Operation	operator: 46 operands: 21
18	Operation	operator: 46 operands: 22
19	ExprTuple	53, 23
20	ExprTuple	53, 24
21	ExprTuple	53, 25
22	ExprTuple	53, 26
23	Operation	operator: 56 operands: 27
24	Operation	operator: 54 operands: 28
25	Operation	operator: 54 operands: 29
26	Operation	operator: 54 operands: 30
27	ExprTuple	58, 31
28	ExprTuple	32, 33
29	ExprTuple	58, 40
30	ExprTuple	34, 35
31	Operation	operator: 46 operands: 36
32	Variable
33	Operation	operator: 48 operands: 37
34	Literal
35	Operation	operator: 48 operands: 38
36	ExprTuple	53, 59
37	ExprTuple	39, 58
38	ExprTuple	40, 58
39	Operation	operator: 56 operands: 41
40	Operation	operator: 56 operands: 42
41	ExprTuple	53, 43
42	ExprTuple	44, 45
43	Operation	operator: 46 operands: 47
44	Operation	operator: 48 operands: 49
45	Operation	operator: 62 operand: 53
46	Literal
47	ExprTuple	53, 51
48	Literal
49	ExprTuple	58, 52
50	ExprTuple	53
51	Operation	operator: 54 operands: 55
52	Operation	operator: 56 operands: 57
53	Literal
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60, 61
58	Literal
59	Literal
60	Literal
61	Operation	operator: 62 operand: 64
62	Literal
63	ExprTuple	64
64	Literal