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 Function, a, b, c, f, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, Sum, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = Function(f, [subtract(x, c)]), domain = Interval(Add(a, c), Add(b, c)))), 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, c \in \mathbb{Z}}~\left(\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\sum_{x = a + c}^{b + c} f\left(x - c\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	parameters: 4 body: 5
4	ExprTuple	54, 55, 56
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: 18 operand: 23
13	Operation	operator: 18 operand: 24
14	Operation	operator: 36 operands: 20
15	Operation	operator: 36 operands: 21
16	Operation	operator: 36 operands: 22
17	ExprTuple	23
18	Literal
19	ExprTuple	24
20	ExprTuple	54, 25
21	ExprTuple	55, 25
22	ExprTuple	56, 25
23	Lambda	parameter: 45 body: 26
24	Lambda	parameter: 45 body: 27
25	Literal
26	Conditional	value: 28 condition: 29
27	Conditional	value: 30 condition: 31
28	Operation	operator: 34 operand: 45
29	Operation	operator: 36 operands: 33
30	Operation	operator: 34 operand: 39
31	Operation	operator: 36 operands: 37
32	ExprTuple	45
33	ExprTuple	45, 38
34	Variable
35	ExprTuple	39
36	Literal
37	ExprTuple	45, 40
38	Operation	operator: 43 operands: 41
39	Operation	operator: 52 operands: 42
40	Operation	operator: 43 operands: 44
41	ExprTuple	54, 55
42	ExprTuple	45, 46
43	Literal
44	ExprTuple	47, 48
45	Variable
46	Operation	operator: 49 operand: 56
47	Operation	operator: 52 operands: 51
48	Operation	operator: 52 operands: 53
49	Literal
50	ExprTuple	56
51	ExprTuple	54, 56
52	Literal
53	ExprTuple	55, 56
54	Variable
55	Variable
56	Variable