Expression of type ExprTuple

from the theory of proveit.logic.sets.cartesian_products

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, m, x
from proveit.core_expr_types import A_1_to_m, a_1_to_m
from proveit.logic import And, CartProd, Equals, Forall, InSet
from proveit.logic.sets.cartesian_products import a_in_A__1_to_m
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m, a_1_to_m], instance_expr = Equals(InSet(x, CartProd(A_1_to_m)), And(Equals(x, [a_1_to_m]), a_in_A__1_to_m)).with_wrapping_at(2)), InSet(m, NaturalPos))))

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(m \mapsto \left\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}, a_{1}, a_{2}, \ldots, a_{m}}~\left(\begin{array}{c} \begin{array}{l} \left(x \in \left(A_{1} \times  A_{2} \times  \ldots \times  A_{m}\right)\right) =  \\ \left(\left(x = \left(a_{1}, a_{2}, \ldots, a_{m}\right)\right)\land \left(a_{1} \in A_{1}\right) \land  \left(a_{2} \in A_{2}\right) \land  \ldots \land  \left(a_{m} \in A_{m}\right)\right) \end{array} \end{array}\right) \textrm{ if } m \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: 37 body: 3
2	ExprTuple	37
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 33 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	37, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	28, 27, 32
12	Operation	operator: 24 operands: 13
13	ExprTuple	14, 15
14	Operation	operator: 33 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	28, 19
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	ExprRange	lambda_map: 26 start_index: 36 end_index: 37
22	Literal
23	ExprTuple	27
24	Literal
25	ExprTuple	28, 29
26	Lambda	parameter: 43 body: 30
27	ExprRange	lambda_map: 31 start_index: 36 end_index: 37
28	Variable
29	ExprTuple	32
30	Operation	operator: 33 operands: 34
31	Lambda	parameter: 43 body: 38
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	Literal
34	ExprTuple	39, 38
35	Lambda	parameter: 43 body: 39
36	Literal
37	Variable
38	IndexedVar	variable: 40 index: 43
39	IndexedVar	variable: 41 index: 43
40	Variable
41	Variable
42	ExprTuple	43
43	Variable