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, f, i
from proveit.core_expr_types import Len, f_1_to_i
from proveit.logic import Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f], instance_expr = InSet(Len(operands = [f_1_to_i]), Natural)), InSet(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\{\forall_{f}~\left(|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right)\right)| \in \mathbb{N}\right) \textrm{ if } i \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 operand: 6
2	Operation	operator: 9 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	18, 12
6	Lambda	parameter: 20 body: 8
7	ExprTuple	20
8	Operation	operator: 9 operands: 10
9	Literal
10	ExprTuple	11, 12
11	Operation	operator: 13 operands: 14
12	Literal
13	Literal
14	ExprTuple	15
15	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
16	Lambda	parameter: 22 body: 19
17	Literal
18	Variable
19	Operation	operator: 20 operand: 22
20	Variable
21	ExprTuple	22
22	Variable