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 Conditional, ExprTuple, Lambda, a, b, i, x
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Integer, Interval, Mult, Neg, Sum, one

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(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), And(InSet(a, Integer), InSet(b, 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())

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