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, f, g, k, l, m, n
from proveit.logic import Equals, Forall
from proveit.numbers import Interval, Sum

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = [l]
sub_expr3 = Interval(m, n)
expr = ExprTuple(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)))

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(\forall_{k \in \{m~\ldotp \ldotp~n\}}~\left(f\left(k\right) = g\left(k\right)\right), \left(\sum_{l = m}^{n} f\left(l\right)\right) = \left(\sum_{l = m}^{n} g\left(l\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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