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, x
from proveit.core_expr_types import Len, f_i_to_j
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Natural, Neg, two

# build up the expression from sub-expressions
expr = Conditional(Equals(Len(operands = [f_i_to_j, x]), Add(j, Neg(i), two)), InSet(Len(operands = [f_i_to_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\{|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = \left(j - i + 2\right) \textrm{ if } |\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\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	Operation	operator: 14 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	19, 16
12	Literal
13	ExprTuple	23, 17, 18
14	Literal
15	ExprTuple	19
16	Variable
17	Operation	operator: 20 operand: 24
18	Literal
19	ExprRange	lambda_map: 22 start_index: 24 end_index: 23
20	Literal
21	ExprTuple	24
22	Lambda	parameter: 28 body: 25
23	Variable
24	Variable
25	Operation	operator: 26 operand: 28
26	Variable
27	ExprTuple	28
28	Variable