Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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