Expression of type Forall

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 x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall, InSet, Intersect
from proveit.logic.sets import x_in_every_A

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = 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())

\forall_{x, A_{1}, A_{2}, \ldots, A_{m}}~\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()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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