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 Abs, Exp, Mod, Mult, Round, four, frac, greater, pi, two
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = greater(Exp(Abs(SubIndexed(_alpha, [Mod(Round(Mult(_two_pow_t, _phase)), _two_pow_t)])), two), frac(four, Exp(pi, 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())

\left|\alpha_{round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t}}\right|^{2} > \frac{4}{\pi^{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	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: 5 operands: 6
4	Operation	operator: 29 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 31
8	Literal
9	Operation	operator: 29 operands: 11
10	Operation	operator: 12 operand: 15
11	ExprTuple	14, 31
12	Literal
13	ExprTuple	15
14	Literal
15	Operation	operator: 16 operand: 18
16	Literal
17	ExprTuple	18
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 27
21	Operation	operator: 22 operand: 24
22	Literal
23	ExprTuple	24
24	Operation	operator: 25 operands: 26
25	Literal
26	ExprTuple	27, 28
27	Operation	operator: 29 operands: 30
28	Literal
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Literal