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 c
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.logic import Equals, Forall, Set

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c, d_1_to_k], instance_expr = Equals(Set(a_1_to_i, b_1_to_j, c, d_1_to_k), Set(a_1_to_i, c, b_1_to_j, d_1_to_k)))

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_{i}, b_{1}, b_{2}, \ldots, b_{j}, c, d_{1}, d_{2}, \ldots, d_{k}}~\left(\left\{a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j}, c,d_{1}, d_{2}, \ldots, d_{k}\right\} = \left\{a_{1}, a_{2}, \ldots, a_{i}, c,b_{1}, b_{2}, \ldots, b_{j},d_{1}, d_{2}, \ldots, d_{k}\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: 9 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, 14, 13, 15
10	Literal
11	ExprTuple	12, 13, 14, 15
12	ExprRange	lambda_map: 16 start_index: 21 end_index: 17
13	Variable
14	ExprRange	lambda_map: 18 start_index: 21 end_index: 19
15	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
16	Lambda	parameter: 30 body: 23
17	Variable
18	Lambda	parameter: 30 body: 24
19	Variable
20	Lambda	parameter: 30 body: 25
21	Literal
22	Variable
23	IndexedVar	variable: 26 index: 30
24	IndexedVar	variable: 27 index: 30
25	IndexedVar	variable: 28 index: 30
26	Variable
27	Variable
28	Variable
29	ExprTuple	30
30	Variable