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, 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(ModAbs(subtract(frac(m, _two_pow_t), _phase), one), frac(Exp(two, subtract(_t, _n)), _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|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1} \leq \frac{2^{t - n}}{2^{t}}

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