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 import l
from proveit.numbers import Exp, Less, frac, one, subtract, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor

# build up the expression from sub-expressions
expr = Less(frac(one, Exp(_diff_l_scaled_delta_floor, two)), frac(one, Exp(subtract(l, one), two)))

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())

\frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} < \frac{1}{\left(l - 1\right)^{2}}

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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	24, 8
6	Literal
7	ExprTuple	24, 9
8	Operation	operator: 29 operands: 10
9	Operation	operator: 29 operands: 11
10	ExprTuple	12, 33
11	ExprTuple	13, 33
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	18, 17
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 21 operand: 23
18	Variable
19	Operation	operator: 21 operand: 24
20	ExprTuple	23
21	Literal
22	ExprTuple	24
23	Operation	operator: 25 operands: 26
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operand: 35
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35
33	Literal
34	Literal
35	Literal