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, three, 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(Add(Mult(three, _eps), one), Variable("_a", latex_format = r"{_{-}a}")))))

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{\left(3 \cdot \epsilon\right) + 1}{{_{-}a}}\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: 47 operands: 5
4	Operation	operator: 47 operands: 6
5	ExprTuple	46, 7
6	ExprTuple	46, 8, 9
7	Operation	operator: 51 operand: 13
8	Operation	operator: 51 operand: 14
9	Operation	operator: 51 operand: 15
10	ExprTuple	13
11	ExprTuple	14
12	ExprTuple	15
13	Operation	operator: 34 operands: 16
14	Operation	operator: 22 operands: 17
15	Operation	operator: 22 operands: 18
16	ExprTuple	38, 19
17	ExprTuple	46, 20
18	ExprTuple	46, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 34 operands: 24
21	Operation	operator: 34 operands: 25
22	Literal
23	ExprTuple	26, 27
24	ExprTuple	44, 33
25	ExprTuple	28, 29
26	Operation	operator: 47 operands: 30
27	Variable
28	Literal
29	Operation	operator: 41 operands: 31
30	ExprTuple	32, 46
31	ExprTuple	33, 44
32	Operation	operator: 34 operands: 35
33	Operation	operator: 47 operands: 36
34	Literal
35	ExprTuple	37, 38
36	ExprTuple	39, 40
37	Literal
38	Literal
39	Operation	operator: 41 operands: 42
40	Operation	operator: 51 operand: 46
41	Literal
42	ExprTuple	44, 45
43	ExprTuple	46
44	Literal
45	Operation	operator: 47 operands: 48
46	Literal
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Operation	operator: 51 operand: 53
51	Literal
52	ExprTuple	53
53	Literal