Expression of type Lambda

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, Lambda, 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 = Lambda(n, 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())

n \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 24 body: 2
1	ExprTuple	24
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 25 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	24, 28
8	Lambda	parameters: 18 body: 9
9	Conditional	value: 10 condition: 11
10	Operation	operator: 25 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 28
13	Literal
14	ExprTuple	16
15	Operation	operator: 17 operands: 18
16	ExprRange	lambda_map: 19 start_index: 23 end_index: 24
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 31 body: 21
20	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
21	Operation	operator: 25 operands: 26
22	Lambda	parameter: 31 body: 27
23	Literal
24	Variable
25	Literal
26	ExprTuple	27, 28
27	IndexedVar	variable: 29 index: 31
28	Literal
29	Variable
30	ExprTuple	31
31	Variable