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, Lambda, k, m
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, one, subtract

# build up the expression from sub-expressions
expr = Equals(Lambda(k, Conditional(k, InSet(k, Interval(one, subtract(Add(m, one), one))))), Lambda(k, Conditional(k, InSet(k, Interval(one, m))))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left[k \mapsto \left\{k \textrm{ if } k \in \{1~\ldotp \ldotp~\left(m + 1\right) - 1\}\right..\right] =  \\ \left[k \mapsto \left\{k \textrm{ if } k \in \{1~\ldotp \ldotp~m\}\right..\right] \end{array} \end{array}

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.	()	(2)	('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	Lambda	parameter: 14 body: 5
4	Lambda	parameter: 14 body: 7
5	Conditional	value: 14 condition: 8
6	ExprTuple	14
7	Conditional	value: 14 condition: 9
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	14, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 17 operands: 16
14	Variable
15	Operation	operator: 17 operands: 18
16	ExprTuple	28, 19
17	Literal
18	ExprTuple	28, 27
19	Operation	operator: 23 operands: 20
20	ExprTuple	21, 22
21	Operation	operator: 23 operands: 24
22	Operation	operator: 25 operand: 28
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	28
27	Variable
28	Literal