Expression of type Forall

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.core_expr_types import a_1_to_m, b_1_to_n
from proveit.logic import Forall, Set, SubsetEq

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_m, b_1_to_n], instance_expr = SubsetEq(Set(a_1_to_m), Set(a_1_to_m, b_1_to_n)))

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_{a_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{n}}~\left(\left\{a_{1}, a_{2}, \ldots, a_{m}\right\} \subseteq \left\{a_{1}, a_{2}, \ldots, a_{m},b_{1}, b_{2}, \ldots, b_{n}\right\}\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: 11 body: 4
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 10 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12
10	Literal
11	ExprTuple	12, 13
12	ExprRange	lambda_map: 14 start_index: 17 end_index: 15
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
14	Lambda	parameter: 24 body: 19
15	Variable
16	Lambda	parameter: 24 body: 20
17	Literal
18	Variable
19	IndexedVar	variable: 21 index: 24
20	IndexedVar	variable: 22 index: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable