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 Variable, m
from proveit.numbers import Floor, ModAbs, Mult, greater_eq, 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 = greater_eq(ModAbs(Variable("_a", latex_format = r"{_{-}a}"), _two_pow_t), subtract(ModAbs(subtract(m, sub_expr1), _two_pow_t), ModAbs(subtract(m, Floor(sub_expr1)), _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|{_{-}a}\right|_{\textup{mod}\thinspace 2^{t}} \geq \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)

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: 19 operands: 5
4	Operation	operator: 15 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 31
7	Operation	operator: 15 operands: 10
8	Operation	operator: 23 operand: 13
9	Variable
10	ExprTuple	12, 31
11	ExprTuple	13
12	Operation	operator: 19 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	21, 17
15	Literal
16	ExprTuple	18, 31
17	Operation	operator: 23 operand: 28
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21, 22
21	Variable
22	Operation	operator: 23 operand: 25
23	Literal
24	ExprTuple	25
25	Operation	operator: 26 operand: 28
26	Literal
27	ExprTuple	28
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Operation	operator: 33 operands: 34
32	Literal
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Literal