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 InSet, Intersect
from proveit.logic.sets import x_in_every_A

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

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