Expression of type Conditional

from the theory of proveit.core_expr_types.tuples

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, i, j, k
from proveit.core_expr_types import partition_equiv
from proveit.logic import And, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = Conditional(partition_equiv, And(InSet(subtract(Add(j, one), i), Natural), InSet(subtract(k, j), Natural)))

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\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(k\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right),f\left(j + 1\right), f\left(j + 2\right), \ldots, f\left(k\right)\right) \end{array} \end{array} \textrm{ if } \left(\left(j + 1\right) - i\right) \in \mathbb{N} ,  \left(k - j\right) \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	ExprTuple	11
8	ExprTuple	12, 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprRange	lambda_map: 17 start_index: 37 end_index: 28
12	ExprRange	lambda_map: 17 start_index: 37 end_index: 38
13	ExprRange	lambda_map: 17 start_index: 26 end_index: 28
14	ExprTuple	18, 20
15	Literal
16	ExprTuple	19, 20
17	Lambda	parameter: 30 body: 21
18	Operation	operator: 31 operands: 22
19	Operation	operator: 31 operands: 23
20	Literal
21	Operation	operator: 24 operand: 30
22	ExprTuple	26, 27
23	ExprTuple	28, 29
24	Variable
25	ExprTuple	30
26	Operation	operator: 31 operands: 32
27	Operation	operator: 34 operand: 37
28	Variable
29	Operation	operator: 34 operand: 38
30	Variable
31	Literal
32	ExprTuple	38, 36
33	ExprTuple	37
34	Literal
35	ExprTuple	38
36	Literal
37	Variable
38	Variable