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, n
from proveit.numbers import Exp, LessEq, ModAbs, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import phase, two_pow_t

# build up the expression from sub-expressions
expr = LessEq(ModAbs(subtract(frac(m, two_pow_t), phase), one), Exp(two, Neg(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|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1} \leq 2^{-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: 24 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	26, 10
8	Operation	operator: 11 operands: 12
9	Literal
10	Operation	operator: 19 operand: 16
11	Literal
12	ExprTuple	14, 15
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operand: 23
16	Variable
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	Variable
22	Operation	operator: 24 operands: 25
23	Variable
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Variable