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
from proveit.core_expr_types import Len, f_i_to_j, i_to_j_len
from proveit.logic import InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(InSet(Len(operands = [f_i_to_j]), Natural), InSet(i_to_j_len, 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)\right)| \in \mathbb{N} \textrm{ if } \left(j - i + 1\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 8
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operands: 12
8	Literal
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	17, 14, 15
13	ExprRange	lambda_map: 16 start_index: 21 end_index: 17
14	Operation	operator: 18 operand: 21
15	Literal
16	Lambda	parameter: 24 body: 20
17	Variable
18	Literal
19	ExprTuple	21
20	Operation	operator: 22 operand: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable