Expression of type Forall

from the theory of proveit.numbers.multiplication

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 n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, Forall, Set
from proveit.numbers import Add, Mult

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_n], instance_expr = Equals(Add(a_1_to_n), Mult(x, n)), domain = Set(x))

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_{n} \in \left\{x\right\}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{n}\right) = \left(x \cdot 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: 15 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprRange	lambda_map: 18 start_index: 22 end_index: 23
14	Literal
15	ExprTuple	19
16	Literal
17	ExprTuple	33, 23
18	Lambda	parameter: 32 body: 20
19	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
20	Operation	operator: 24 operands: 25
21	Lambda	parameter: 32 body: 26
22	Literal
23	Variable
24	Literal
25	ExprTuple	26, 27
26	IndexedVar	variable: 28 index: 32
27	Operation	operator: 30 operand: 33
28	Variable
29	ExprTuple	32
30	Literal
31	ExprTuple	33
32	Variable
33	Variable