Expression of type Lambda

from the theory of proveit.logic.sets.intersection

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 A_1_to_m
from proveit.logic import Intersect, NotInSet
from proveit.logic.sets import x_notin_some_A

# build up the expression from sub-expressions
expr = Lambda([x, A_1_to_m], Conditional(NotInSet(x, Intersect(A_1_to_m)), x_notin_some_A))

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