Expression of type Lambda

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, Lambda, c, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c, d_1_to_k], instance_expr = Equals(Set(a_1_to_i, b_1_to_j, c, d_1_to_k), Set(a_1_to_i, c, b_1_to_j, d_1_to_k))), And(InSet(i, Natural), InSet(j, Natural), InSet(k, 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(i, j, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c, d_{1}, d_{2}, \ldots, d_{k}}~\left(\left\{a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j}, c,d_{1}, d_{2}, \ldots, d_{k}\right\} = \left\{a_{1}, a_{2}, \ldots, a_{i}, c,b_{1}, b_{2}, \ldots, b_{j},d_{1}, d_{2}, \ldots, d_{k}\right\}\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	31, 33, 36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 23 body: 13
10	Operation	operator: 16 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	31, 20
15	ExprTuple	33, 20
16	Literal
17	ExprTuple	36, 20
18	Literal
19	ExprTuple	21, 22
20	Literal
21	Operation	operator: 24 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 28, 27, 29
24	Literal
25	ExprTuple	26, 27, 28, 29
26	ExprRange	lambda_map: 30 start_index: 35 end_index: 31
27	Variable
28	ExprRange	lambda_map: 32 start_index: 35 end_index: 33
29	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
30	Lambda	parameter: 44 body: 37
31	Variable
32	Lambda	parameter: 44 body: 38
33	Variable
34	Lambda	parameter: 44 body: 39
35	Literal
36	Variable
37	IndexedVar	variable: 40 index: 44
38	IndexedVar	variable: 41 index: 44
39	IndexedVar	variable: 42 index: 44
40	Variable
41	Variable
42	Variable
43	ExprTuple	44
44	Variable