Expression of type Forall

from the theory of proveit.numbers.division

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, IndexedVar, Variable, n, x, y
from proveit.core_expr_types import x_1_to_n
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import Add, Complex, frac, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [x_1_to_n, y], instance_expr = Equals(frac(Add(x_1_to_n), y), Add(ExprRange(sub_expr1, frac(IndexedVar(x, sub_expr1), y), one, n))), domain = Complex, condition = NotEquals(y, zero))

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_{x_{1}, x_{2}, \ldots, x_{n}, y \in \mathbb{C}~|~y \neq 0}~\left(\frac{x_{1} +  x_{2} +  \ldots +  x_{n}}{y} = \left(\frac{x_{1}}{y} +  \frac{x_{2}}{y} +  \ldots +  \frac{x_{n}}{y}\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	32, 41
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, 16
12	Operation	operator: 38 operands: 17
13	Operation	operator: 27 operands: 18
14	ExprRange	lambda_map: 19 start_index: 36 end_index: 37
15	Operation	operator: 30 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	23, 41
18	ExprTuple	24
19	Lambda	parameter: 44 body: 25
20	ExprTuple	41, 34
21	Literal
22	ExprTuple	41, 26
23	Operation	operator: 27 operands: 28
24	ExprRange	lambda_map: 29 start_index: 36 end_index: 37
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	ExprTuple	32
29	Lambda	parameter: 44 body: 33
30	Literal
31	ExprTuple	40, 34
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	Lambda	parameter: 44 body: 40
36	Literal
37	Variable
38	Literal
39	ExprTuple	40, 41
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable