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, Function, Lambda, f, g, k, l, m, n
from proveit.logic import Equals, Forall, Implies
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([f, g], Forall(instance_param_or_params = [m, n], instance_expr = 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))), 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())

\left(\left(f, g\right) \mapsto \left[\forall_{m, n \in \mathbb{Z}}~\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)\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	parameters: 2 body: 3
2	ExprTuple	45, 46
3	Operation	operator: 17 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 54 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 17 operand: 22
14	Operation	operator: 34 operands: 19
15	Operation	operator: 48 operands: 20
16	Operation	operator: 48 operands: 21
17	Literal
18	ExprTuple	22
19	ExprTuple	23, 24
20	ExprTuple	55, 25
21	ExprTuple	56, 25
22	Lambda	parameter: 50 body: 26
23	Operation	operator: 28 operand: 32
24	Operation	operator: 28 operand: 33
25	Literal
26	Conditional	value: 30 condition: 31
27	ExprTuple	32
28	Literal
29	ExprTuple	33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 48 operands: 36
32	Lambda	parameter: 51 body: 37
33	Lambda	parameter: 51 body: 38
34	Literal
35	ExprTuple	39, 40
36	ExprTuple	50, 52
37	Conditional	value: 41 condition: 43
38	Conditional	value: 42 condition: 43
39	Operation	operator: 45 operand: 50
40	Operation	operator: 46 operand: 50
41	Operation	operator: 45 operand: 51
42	Operation	operator: 46 operand: 51
43	Operation	operator: 48 operands: 49
44	ExprTuple	50
45	Variable
46	Variable
47	ExprTuple	51
48	Literal
49	ExprTuple	51, 52
50	Variable
51	Variable
52	Operation	operator: 53 operands: 54
53	Literal
54	ExprTuple	55, 56
55	Variable
56	Variable