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, frac, greater, one, subtract, three, two
from proveit.physics.quantum.QPE import _eps

# build up the expression from sub-expressions
expr = greater(subtract(one, Mult(_eps, frac(Add(Mult(three, _eps), one), Exp(Add(Mult(two, _eps), one), 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 - \left(\epsilon \cdot \frac{\left(3 \cdot \epsilon\right) + 1}{\left(\left(2 \cdot \epsilon\right) + 1\right)^{2}}\right)\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: 25 operands: 5
4	Operation	operator: 25 operands: 6
5	ExprTuple	29, 7
6	ExprTuple	29, 8
7	Operation	operator: 10 operand: 33
8	Operation	operator: 10 operand: 12
9	ExprTuple	33
10	Literal
11	ExprTuple	12
12	Operation	operator: 30 operands: 13
13	ExprTuple	33, 14
14	Operation	operator: 15 operands: 16
15	Literal
16	ExprTuple	17, 18
17	Operation	operator: 25 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 29
20	Literal
21	ExprTuple	23, 32
22	Operation	operator: 30 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 33
25	Literal
26	ExprTuple	28, 29
27	Literal
28	Operation	operator: 30 operands: 31
29	Literal
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Literal