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 m
from proveit.numbers import Exp, LessEq, ModAbs, Mult, frac, one, subtract, two
from proveit.physics.quantum.QPE import _n, _phase, _t, _two_pow_t

# build up the expression from sub-expressions
expr = LessEq(Mult(_two_pow_t, ModAbs(subtract(frac(m, _two_pow_t), _phase), one)), Exp(two, subtract(_t, _n)))

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(2^{t} \cdot \left|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1}\right) \leq 2^{t - n}

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