Expression of type Forall

from the theory of proveit.numbers.summation

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 a, b, i, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, Interval, Mult, Neg, Sum, one

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x], instance_expr = Equals(Sum(index_or_indices = [i], summand = x, domain = Interval(a, b)), Mult(Add(b, Neg(a), one), x)), domain = 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_{x \in \mathbb{C}}~\left(\left(\sum_{i = a}^{b} x\right) = \left(\left(b - a + 1\right) \cdot x\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	parameter: 24 body: 5
4	ExprTuple	24
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 28 operands: 10
8	Literal
9	ExprTuple	11, 12
10	ExprTuple	24, 13
11	Operation	operator: 14 operand: 18
12	Operation	operator: 16 operands: 17
13	Literal
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 24
18	Lambda	parameter: 32 body: 21
19	Operation	operator: 22 operands: 23
20	ExprTuple	32
21	Conditional	value: 24 condition: 25
22	Literal
23	ExprTuple	37, 26, 27
24	Variable
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operand: 36
27	Literal
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	36
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Variable