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, ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import Mult, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(Mult(a_1_to_n), Natural), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Natural), one, n)))

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(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \mathbb{N} \textrm{ if } \left(a_{1} \in \mathbb{N}\right) \land  \left(a_{2} \in \mathbb{N}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{N}\right)\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: 16 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 19
4	Literal
5	ExprTuple	7
6	Operation	operator: 8 operands: 9
7	ExprRange	lambda_map: 10 start_index: 14 end_index: 15
8	Literal
9	ExprTuple	11
10	Lambda	parameter: 22 body: 12
11	ExprRange	lambda_map: 13 start_index: 14 end_index: 15
12	Operation	operator: 16 operands: 17
13	Lambda	parameter: 22 body: 18
14	Literal
15	Variable
16	Literal
17	ExprTuple	18, 19
18	IndexedVar	variable: 20 index: 22
19	Literal
20	Variable
21	ExprTuple	22
22	Variable