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
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import NotInSet, ProperSubset, Set

# build up the expression from sub-expressions
sub_expr1 = Set(a_1_to_m)
expr = Lambda([a_1_to_m, b, c_1_to_n], Conditional(ProperSubset(sub_expr1, Set(a_1_to_m, b, c_1_to_n)), NotInSet(b, sub_expr1)))

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(a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}\right) \mapsto \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\} \textrm{ if } b \notin \left\{a_{1}, a_{2}, \ldots, a_{m}\right\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 10 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	9, 8
6	Literal
7	ExprTuple	13, 9
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	15, 13, 14
11	Literal
12	ExprTuple	15
13	Variable
14	ExprRange	lambda_map: 16 start_index: 19 end_index: 17
15	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
16	Lambda	parameter: 26 body: 21
17	Variable
18	Lambda	parameter: 26 body: 22
19	Literal
20	Variable
21	IndexedVar	variable: 23 index: 26
22	IndexedVar	variable: 24 index: 26
23	Variable
24	Variable
25	ExprTuple	26
26	Variable