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 Lambda, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, 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], Equals(InSet(x, Intersect(A_1_to_m)), x_in_every_A).with_wrapping_at(2))

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(\begin{array}{c} \begin{array}{l} \left(x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right)\right) =  \\ \left(\left(x \in A_{1}\right) \land  \left(x \in A_{2}\right) \land  \ldots \land  \left(x \in A_{m}\right)\right) \end{array} \end{array}\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	22, 15
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 20 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	22, 10
8	Literal
9	ExprTuple	11
10	Operation	operator: 12 operands: 13
11	ExprRange	lambda_map: 14 start_index: 18 end_index: 19
12	Literal
13	ExprTuple	15
14	Lambda	parameter: 26 body: 16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 26 body: 23
18	Literal
19	Variable
20	Literal
21	ExprTuple	22, 23
22	Variable
23	IndexedVar	variable: 24 index: 26
24	Variable
25	ExprTuple	26
26	Variable