Expression of type Less

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, 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(Add(one, Neg(frac(one, Mult(two, sub_expr1))), Neg(frac(one, Mult(four, Exp(sub_expr1, two))))), subtract(one, _eps))

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) > \left(1 - \epsilon\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: 37 operands: 5
4	Operation	operator: 37 operands: 6
5	ExprTuple	36, 7
6	ExprTuple	36, 8, 9
7	Operation	operator: 41 operand: 13
8	Operation	operator: 41 operand: 14
9	Operation	operator: 41 operand: 15
10	ExprTuple	13
11	ExprTuple	14
12	ExprTuple	15
13	Literal
14	Operation	operator: 17 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	36, 19
17	Literal
18	ExprTuple	36, 20
19	Operation	operator: 22 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	34, 27
22	Literal
23	ExprTuple	24, 25
24	Literal
25	Operation	operator: 31 operands: 26
26	ExprTuple	27, 34
27	Operation	operator: 37 operands: 28
28	ExprTuple	29, 30
29	Operation	operator: 31 operands: 32
30	Operation	operator: 41 operand: 36
31	Literal
32	ExprTuple	34, 35
33	ExprTuple	36
34	Literal
35	Operation	operator: 37 operands: 38
36	Literal
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operand: 43
41	Literal
42	ExprTuple	43
43	Literal