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 l
from proveit.numbers import Add, LessEq, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _delta_b, _two_pow__t_minus_one, _two_pow_t

# build up the expression from sub-expressions
expr = LessEq(subtract(_delta_b, frac(l, _two_pow_t)), subtract(frac(one, two), frac(Add(Neg(_two_pow__t_minus_one), one), _two_pow_t)))

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(\delta_{b} - \frac{l}{2^{t}}\right) \leq \left(\frac{1}{2} - \frac{-2^{t - 1} + 1}{2^{t}}\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: 34 operands: 5
4	Operation	operator: 34 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10
7	Operation	operator: 11 operand: 16
8	Operation	operator: 38 operand: 17
9	Operation	operator: 20 operands: 14
10	Operation	operator: 38 operand: 18
11	Literal
12	ExprTuple	16
13	ExprTuple	17
14	ExprTuple	40, 32
15	ExprTuple	18
16	Variable
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 24
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Operation	operator: 34 operands: 25
24	Operation	operator: 30 operands: 26
25	ExprTuple	27, 40
26	ExprTuple	32, 36
27	Operation	operator: 38 operand: 29
28	ExprTuple	29
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Operation	operator: 38 operand: 40
38	Literal
39	ExprTuple	40
40	Literal