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, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import NotInSet, Set
from proveit.logic.sets import x_notequals_all_y

# build up the expression from sub-expressions
expr = Lambda([x, y_1_to_n], Conditional(NotInSet(x, Set(y_1_to_n)), x_notequals_all_y))

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(x, y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\} \textrm{ if } \left(x \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\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: 1 body: 2
1	ExprTuple	21, 14
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	21, 9
7	Literal
8	ExprTuple	10
9	Operation	operator: 11 operands: 12
10	ExprRange	lambda_map: 13 start_index: 17 end_index: 18
11	Literal
12	ExprTuple	14
13	Lambda	parameter: 25 body: 15
14	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
15	Operation	operator: 19 operands: 20
16	Lambda	parameter: 25 body: 22
17	Literal
18	Variable
19	Literal
20	ExprTuple	21, 22
21	Variable
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Variable