Expression of type Conditional

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, 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 = 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\{\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..

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: 30 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	34, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	25, 24, 29
9	Operation	operator: 21 operands: 10
10	ExprTuple	11, 12
11	Operation	operator: 30 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	25, 16
14	Literal
15	ExprTuple	17, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprRange	lambda_map: 23 start_index: 33 end_index: 34
19	Literal
20	ExprTuple	24
21	Literal
22	ExprTuple	25, 26
23	Lambda	parameter: 40 body: 27
24	ExprRange	lambda_map: 28 start_index: 33 end_index: 34
25	Variable
26	ExprTuple	29
27	Operation	operator: 30 operands: 31
28	Lambda	parameter: 40 body: 35
29	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
30	Literal
31	ExprTuple	36, 35
32	Lambda	parameter: 40 body: 36
33	Literal
34	Variable
35	IndexedVar	variable: 37 index: 40
36	IndexedVar	variable: 38 index: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable