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 import b, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m, n], instance_expr = Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n], instance_expr = InSet(b, Set(a_1_to_m, b, c_1_to_n))), domain = Natural)

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_{m, n \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}}~\left(b \in \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\}\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	27, 30
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameters: 22 body: 14
12	Operation	operator: 17 operands: 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	27, 19
16	ExprTuple	30, 19
17	Literal
18	ExprTuple	24, 20
19	Literal
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24, 25
23	ExprRange	lambda_map: 26 start_index: 29 end_index: 27
24	Variable
25	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
26	Lambda	parameter: 36 body: 31
27	Variable
28	Lambda	parameter: 36 body: 32
29	Literal
30	Variable
31	IndexedVar	variable: 33 index: 36
32	IndexedVar	variable: 34 index: 36
33	Variable
34	Variable
35	ExprTuple	36
36	Variable