Expression of type ExprTuple

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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Mult(a_1_to_n), NaturalPos), domain = NaturalPos), 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(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 26 body: 3
2	ExprTuple	26
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 27 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	26, 10
9	Lambda	parameters: 20 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 27 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 30
15	Literal
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	ExprRange	lambda_map: 21 start_index: 25 end_index: 26
19	Literal
20	ExprTuple	22
21	Lambda	parameter: 33 body: 23
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	Operation	operator: 27 operands: 28
24	Lambda	parameter: 33 body: 29
25	Literal
26	Variable
27	Literal
28	ExprTuple	29, 30
29	IndexedVar	variable: 31 index: 33
30	Literal
31	Variable
32	ExprTuple	33
33	Variable