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, Complex, Mult, Natural

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

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_{n \in \mathbb{N}, x \in \mathbb{C}}~\left[\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)\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	36, 46
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 22 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameters: 28 body: 13
11	Operation	operator: 37 operands: 14
12	Operation	operator: 37 operands: 15
13	Conditional	value: 16 condition: 17
14	ExprTuple	36, 18
15	ExprTuple	46, 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	Literal
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	ExprRange	lambda_map: 31 start_index: 35 end_index: 36
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	46, 36
31	Lambda	parameter: 45 body: 33
32	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
33	Operation	operator: 37 operands: 38
34	Lambda	parameter: 45 body: 39
35	Literal
36	Variable
37	Literal
38	ExprTuple	39, 40
39	IndexedVar	variable: 41 index: 45
40	Operation	operator: 43 operand: 46
41	Variable
42	ExprTuple	45
43	Literal
44	ExprTuple	46
45	Variable
46	Variable