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, LessEq, Mult, Neg, four, frac, 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)
sub_expr2 = Neg(frac(one, Mult(four, Exp(sub_expr1, two))))
expr = LessEq(Add(one, Neg(frac(one, Mult(two, Add(one, frac(one, Mult(two, _eps)))))), sub_expr2), Add(one, Neg(frac(one, Mult(two, sub_expr1))), sub_expr2))

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(1 + \frac{1}{2 \cdot \epsilon}\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\right)^{2}}\right) \leq \left(1 - \frac{1}{2 \cdot \left(2^{t - n} - 1\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\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	normal	('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, 9
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: 32 operands: 16
14	Operation	operator: 32 operands: 17
15	Operation	operator: 32 operands: 18
16	ExprTuple	46, 19
17	ExprTuple	46, 20
18	ExprTuple	46, 21
19	Operation	operator: 38 operands: 22
20	Operation	operator: 38 operands: 23
21	Operation	operator: 38 operands: 24
22	ExprTuple	44, 25
23	ExprTuple	44, 31
24	ExprTuple	26, 27
25	Operation	operator: 47 operands: 28
26	Literal
27	Operation	operator: 40 operands: 29
28	ExprTuple	46, 30
29	ExprTuple	31, 44
30	Operation	operator: 32 operands: 33
31	Operation	operator: 47 operands: 34
32	Literal
33	ExprTuple	46, 35
34	ExprTuple	36, 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 51 operand: 46
38	Literal
39	ExprTuple	44, 43
40	Literal
41	ExprTuple	44, 45
42	ExprTuple	46
43	Literal
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