Expression of type ExprTuple

from the theory of proveit.logic.sets.enumeration

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, b, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import And, Forall, InSet, NotInSet, ProperSubset, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = Set(a_1_to_m)
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n], instance_expr = ProperSubset(sub_expr1, Set(a_1_to_m, b, c_1_to_n)), condition = NotInSet(b, sub_expr1)), And(InSet(m, 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())

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