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, Function, Lambda, f, g, k, l, m, n
from proveit.logic import And, Equals, Forall, Implies, InSet
from proveit.numbers import Integer, Interval, Sum

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = [l]
sub_expr3 = Interval(m, n)
expr = ExprTuple(Lambda([m, n], Conditional(Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(f, sub_expr1), Function(g, sub_expr1)), domain = sub_expr3), Equals(Sum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), domain = sub_expr3), Sum(index_or_indices = sub_expr2, summand = Function(g, sub_expr2), domain = sub_expr3))), And(InSet(m, Integer), InSet(n, 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(m, n\right) \mapsto \left\{\left[\forall_{k \in \{m~\ldotp \ldotp~n\}}~\left(f\left(k\right) = g\left(k\right)\right)\right] \Rightarrow \left(\left(\sum_{l = m}^{n} f\left(l\right)\right) = \left(\sum_{l = m}^{n} g\left(l\right)\right)\right) \textrm{ if } m \in \mathbb{Z} ,  n \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: 50 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 13 operand: 18
10	Operation	operator: 30 operands: 15
11	Operation	operator: 44 operands: 16
12	Operation	operator: 44 operands: 17
13	Literal
14	ExprTuple	18
15	ExprTuple	19, 20
16	ExprTuple	51, 21
17	ExprTuple	52, 21
18	Lambda	parameter: 46 body: 22
19	Operation	operator: 24 operand: 28
20	Operation	operator: 24 operand: 29
21	Literal
22	Conditional	value: 26 condition: 27
23	ExprTuple	28
24	Literal
25	ExprTuple	29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 44 operands: 32
28	Lambda	parameter: 47 body: 33
29	Lambda	parameter: 47 body: 34
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	46, 48
33	Conditional	value: 37 condition: 39
34	Conditional	value: 38 condition: 39
35	Operation	operator: 41 operand: 46
36	Operation	operator: 42 operand: 46
37	Operation	operator: 41 operand: 47
38	Operation	operator: 42 operand: 47
39	Operation	operator: 44 operands: 45
40	ExprTuple	46
41	Variable
42	Variable
43	ExprTuple	47
44	Literal
45	ExprTuple	47, 48
46	Variable
47	Variable
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Variable
52	Variable