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, Integer, Interval, Mult, Neg, Sum, one

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_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), domain = Integer)

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, b \in \mathbb{Z}}~\left[\forall_{x \in \mathbb{C}}~\left(\left(\sum_{i = a}^{b} x\right) = \left(\left(b - a + 1\right) \cdot x\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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 47 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 36 body: 14
11	Operation	operator: 40 operands: 15
12	Operation	operator: 40 operands: 16
13	ExprTuple	36
14	Conditional	value: 17 condition: 18
15	ExprTuple	48, 19
16	ExprTuple	49, 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 40 operands: 22
19	Literal
20	Literal
21	ExprTuple	23, 24
22	ExprTuple	36, 25
23	Operation	operator: 26 operand: 30
24	Operation	operator: 28 operands: 29
25	Literal
26	Literal
27	ExprTuple	30
28	Literal
29	ExprTuple	31, 36
30	Lambda	parameter: 44 body: 33
31	Operation	operator: 34 operands: 35
32	ExprTuple	44
33	Conditional	value: 36 condition: 37
34	Literal
35	ExprTuple	49, 38, 39
36	Variable
37	Operation	operator: 40 operands: 41
38	Operation	operator: 42 operand: 48
39	Literal
40	Literal
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	48
44	Variable
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Variable