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, alpha, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Forall(instance_param_or_params = [alpha], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(Add(b, one), c)))))

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_{\alpha}~\left(\left(\sum_{k = a}^{c} \alpha_{k}\right) = \left(\left(\sum_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 31 body: 5
4	ExprTuple	31
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 17 operand: 12
9	Operation	operator: 44 operands: 11
10	ExprTuple	12
11	ExprTuple	13, 14
12	Lambda	parameter: 36 body: 15
13	Operation	operator: 17 operand: 20
14	Operation	operator: 17 operand: 21
15	Conditional	value: 27 condition: 19
16	ExprTuple	20
17	Literal
18	ExprTuple	21
19	Operation	operator: 33 operands: 22
20	Lambda	parameter: 36 body: 23
21	Lambda	parameter: 36 body: 24
22	ExprTuple	36, 25
23	Conditional	value: 27 condition: 26
24	Conditional	value: 27 condition: 28
25	Operation	operator: 39 operands: 29
26	Operation	operator: 33 operands: 30
27	IndexedVar	variable: 31 index: 36
28	Operation	operator: 33 operands: 34
29	ExprTuple	41, 43
30	ExprTuple	36, 35
31	Variable
32	ExprTuple	36
33	Literal
34	ExprTuple	36, 37
35	Operation	operator: 39 operands: 38
36	Variable
37	Operation	operator: 39 operands: 40
38	ExprTuple	41, 46
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Operation	operator: 44 operands: 45
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Literal