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 ExprRange, Variable, n, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, Mult, Natural, one

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n, x], instance_expr = Equals(Add(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n)), Mult(x, n)), 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(\left(x +  x +  ..\left(n - 3\right) \times.. +  x\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: 4 body: 5
4	ExprTuple	28, 30
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 21 operands: 20
15	Operation	operator: 21 operands: 22
16	Literal
17	ExprTuple	23
18	Literal
19	ExprTuple	30, 28
20	ExprTuple	28, 24
21	Literal
22	ExprTuple	30, 25
23	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
24	Literal
25	Literal
26	Lambda	parameter: 31 body: 30
27	Literal
28	Variable
29	ExprTuple	31
30	Variable
31	Variable