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, d, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n, d], instance_expr = Equals(Set(a_1_to_m, b, c_1_to_n), Set(a_1_to_m, d, c_1_to_n)).with_wrapping_at(2), condition = Equals(b, d)), 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}, d~|~b = d}~\left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{m}, d,c_{1}, c_{2}, \ldots, c_{n}\right\} \end{array} \end{array}\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	34, 37
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: 13 body: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	30, 29, 32, 31
14	Conditional	value: 18 condition: 19
15	ExprTuple	34, 20
16	Literal
17	ExprTuple	37, 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	29, 31
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	30, 29, 32
27	Literal
28	ExprTuple	30, 31, 32
29	Variable
30	ExprRange	lambda_map: 33 start_index: 36 end_index: 34
31	Variable
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	Lambda	parameter: 43 body: 38
34	Variable
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