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 Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f], instance_expr = Equals(Len(operands = [f_1_to_i]), i)), 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)| = i\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	19, 8
7	Lambda	parameter: 21 body: 10
8	Literal
9	ExprTuple	21
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 19
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16
16	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
17	Lambda	parameter: 23 body: 20
18	Literal
19	Variable
20	Operation	operator: 21 operand: 23
21	Variable
22	ExprTuple	23
23	Variable