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
from proveit.core_expr_types import partition_front_equiv
from proveit.logic import InSet
from proveit.numbers import Natural, subtract

# build up the expression from sub-expressions
expr = Conditional(partition_front_equiv, InSet(subtract(j, i), 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(j\right)\right) =  \\ \left(f\left(i\right),f\left(i + 1\right), f\left(i + 2\right), \ldots, f\left(j\right)\right) \end{array} \end{array} \textrm{ if } \left(j - i\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: 20 operands: 14
10	Literal
11	ExprRange	lambda_map: 15 start_index: 27 end_index: 17
12	Operation	operator: 24 operand: 27
13	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
14	ExprTuple	17, 18
15	Lambda	parameter: 28 body: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Operation	operator: 22 operand: 27
19	Operation	operator: 24 operand: 28
20	Literal
21	ExprTuple	27, 26
22	Literal
23	ExprTuple	27
24	Variable
25	ExprTuple	28
26	Literal
27	Variable
28	Variable