Expression of type ExprTuple

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 ExprTuple, Lambda, a, b, f, fa, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Interval, Less, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(f, Forall(instance_param_or_params = [a, b], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Add(fa, Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(Add(a, one), b)))), domain = Integer, condition = Less(a, b))))

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())

\left(f \mapsto \left[\forall_{a, b \in \mathbb{Z}~|~a < b}~\left(\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(f\left(a\right) + \left(\sum_{x = a + 1}^{b} f\left(x\right)\right)\right)\right)\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 40 body: 3
2	ExprTuple	40
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 39 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18
14	Operation	operator: 30 operand: 24
15	Operation	operator: 50 operands: 20
16	Operation	operator: 42 operands: 21
17	Operation	operator: 42 operands: 22
18	Operation	operator: 23 operands: 39
19	ExprTuple	24
20	ExprTuple	25, 26
21	ExprTuple	52, 27
22	ExprTuple	49, 27
23	Literal
24	Lambda	parameter: 44 body: 28
25	Operation	operator: 40 operand: 52
26	Operation	operator: 30 operand: 33
27	Literal
28	Conditional	value: 37 condition: 32
29	ExprTuple	52
30	Literal
31	ExprTuple	33
32	Operation	operator: 42 operands: 34
33	Lambda	parameter: 44 body: 35
34	ExprTuple	44, 36
35	Conditional	value: 37 condition: 38
36	Operation	operator: 46 operands: 39
37	Operation	operator: 40 operand: 44
38	Operation	operator: 42 operands: 43
39	ExprTuple	52, 49
40	Variable
41	ExprTuple	44
42	Literal
43	ExprTuple	44, 45
44	Variable
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Operation	operator: 50 operands: 51
49	Variable
50	Literal
51	ExprTuple	52, 53
52	Variable
53	Literal