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, 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 = 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(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..

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	35, 32
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
9	Lambda	parameters: 25 body: 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	35, 18
14	Literal
15	ExprTuple	32, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	24, 23
21	Literal
22	ExprTuple	28, 24
23	Operation	operator: 26 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	30, 28, 29
26	Literal
27	ExprTuple	30
28	Variable
29	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
30	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
31	Lambda	parameter: 41 body: 36
32	Variable
33	Lambda	parameter: 41 body: 37
34	Literal
35	Variable
36	IndexedVar	variable: 38 index: 41
37	IndexedVar	variable: 39 index: 41
38	Variable
39	Variable
40	ExprTuple	41
41	Variable