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 Floor, LessEq, ModAbs, Mult, one, subtract
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Mult(_two_pow_t, _phase)
expr = LessEq(subtract(ModAbs(subtract(m, sub_expr1), _two_pow_t), ModAbs(subtract(m, Floor(sub_expr1)), _two_pow_t)), one)

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

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