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, d
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import Equals, Forall, Set

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n, d], instance_expr = Equals(Set(a_1_to_m, b, c_1_to_n), Set(a_1_to_m, d, c_1_to_n)).with_wrapping_at(2), condition = Equals(b, d))

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, c_{1}, c_{2}, \ldots, c_{n}, d~|~b = d}~\left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{m}, d,c_{1}, c_{2}, \ldots, c_{n}\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	17, 16, 19, 18
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	16, 18
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	17, 16, 19
14	Literal
15	ExprTuple	17, 18, 19
16	Variable
17	ExprRange	lambda_map: 20 start_index: 23 end_index: 21
18	Variable
19	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
20	Lambda	parameter: 30 body: 25
21	Variable
22	Lambda	parameter: 30 body: 26
23	Literal
24	Variable
25	IndexedVar	variable: 27 index: 30
26	IndexedVar	variable: 28 index: 30
27	Variable
28	Variable
29	ExprTuple	30
30	Variable