Expression of type Equals

from the theory of proveit.numbers.summation

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 Conditional, k
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, eight, nine, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = subtract(k, two)
expr = Equals(Conditional(sub_expr1, InSet(k, Interval(Add(eight, one), nine))), Conditional(sub_expr1, InSet(k, Interval(nine, nine))))

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\{k - 2 \textrm{ if } k \in \{8 + 1~\ldotp \ldotp~9\}\right.. = \left\{k - 2 \textrm{ if } k \in \{9~\ldotp \ldotp~9\}\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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Conditional	value: 6 condition: 5
4	Conditional	value: 6 condition: 7
5	Operation	operator: 10 operands: 8
6	Operation	operator: 24 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	14, 12
9	ExprTuple	14, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 19 operands: 16
13	Operation	operator: 17 operand: 22
14	Variable
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 23
17	Literal
18	ExprTuple	22
19	Literal
20	ExprTuple	23, 23
21	Operation	operator: 24 operands: 25
22	Literal
23	Literal
24	Literal
25	ExprTuple	26, 27
26	Literal
27	Literal