Expression of type Conditional

from the theory of proveit.numbers.numerals.decimals

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, Function, f, i, j
from proveit.core_expr_types import f_i_to_j
from proveit.logic import Equals
from proveit.numbers import Add, one, two

# build up the expression from sub-expressions
sub_expr1 = Add(i, two)
expr = Conditional(Equals([f_i_to_j], [Function(f, [i]), Function(f, [Add(i, one)]), Function(f, [sub_expr1])]), Equals(j, sub_expr1))

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(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)\right) \textrm{ if } j = \left(i + 2\right)\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	13, 19
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	ExprRange	lambda_map: 12 start_index: 27 end_index: 13
9	Operation	operator: 20 operand: 27
10	Operation	operator: 20 operand: 18
11	Operation	operator: 20 operand: 19
12	Lambda	parameter: 25 body: 17
13	Variable
14	ExprTuple	27
15	ExprTuple	18
16	ExprTuple	19
17	Operation	operator: 20 operand: 25
18	Operation	operator: 23 operands: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	ExprTuple	25
22	ExprTuple	27, 26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	Literal
27	Variable
28	Literal