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

# build up the expression from sub-expressions
expr = greater_eq(Neg(frac(one, Mult(two, subtract(Exp(two, subtract(_t, _n)), one)))), Neg(frac(one, Mult(two, Add(one, frac(one, Mult(two, _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(-\frac{1}{2 \cdot \left(2^{t - n} - 1\right)}\right) \geq \left(-\frac{1}{2 \cdot \left(1 + \frac{1}{2 \cdot \epsilon}\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: 38 operand: 7
4	Operation	operator: 38 operand: 8
5	ExprTuple	7
6	ExprTuple	8
7	Operation	operator: 22 operands: 9
8	Operation	operator: 22 operands: 10
9	ExprTuple	29, 11
10	ExprTuple	29, 12
11	Operation	operator: 30 operands: 13
12	Operation	operator: 30 operands: 14
13	ExprTuple	34, 15
14	ExprTuple	34, 16
15	Operation	operator: 32 operands: 17
16	Operation	operator: 32 operands: 18
17	ExprTuple	29, 19
18	ExprTuple	20, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 38 operand: 29
22	Literal
23	ExprTuple	29, 27
24	Literal
25	ExprTuple	34, 28
26	ExprTuple	29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Literal
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Literal
35	Literal
36	Literal
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal