Expression of type Equals

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 e, m
from proveit.logic import Equals, Not
from proveit.numbers import LessEq, ModAbs, greater, subtract
from proveit.physics.quantum.QPE import _b_floor, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = ModAbs(subtract(m, _b_floor), _two_pow_t)
sub_expr2 = LessEq(sub_expr1, e)
expr = Equals(Equals(sub_expr2, Not(greater(sub_expr1, e))), Equals(sub_expr2, sub_expr2))

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(\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq e\right) = (\lnot \left(\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} > e\right))\right) = \left(\left(\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq e\right) = \left(\left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq e\right)\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	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 5 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	8, 7
5	Literal
6	ExprTuple	8, 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	17, 16
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Variable
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Variable
27	Operation	operator: 30 operand: 32
28	Literal
29	Literal
30	Literal
31	ExprTuple	32
32	Literal