Expression of type Conditional

from the theory of proveit.numbers.multiplication

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, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import Mult, Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Mult(a_1_to_n), Natural), domain = Natural), InSet(n, 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_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{N}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \mathbb{N}\right) \textrm{ if } n \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: 23 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	22, 26
6	Lambda	parameters: 16 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 23 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 26
11	Literal
12	ExprTuple	14
13	Operation	operator: 15 operands: 16
14	ExprRange	lambda_map: 17 start_index: 21 end_index: 22
15	Literal
16	ExprTuple	18
17	Lambda	parameter: 29 body: 19
18	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
19	Operation	operator: 23 operands: 24
20	Lambda	parameter: 29 body: 25
21	Literal
22	Variable
23	Literal
24	ExprTuple	25, 26
25	IndexedVar	variable: 27 index: 29
26	Literal
27	Variable
28	ExprTuple	29
29	Variable