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, S, a, b, k, l
from proveit.logic import Forall, Implies
from proveit.numbers import LessEq, Sum
from proveit.numbers.summation import ak, al, bk, bl

# build up the expression from sub-expressions
sub_expr1 = [l]
expr = ExprTuple(Lambda([a, b, S], Implies(Forall(instance_param_or_params = [k], instance_expr = LessEq(ak, bk), domain = S), LessEq(Sum(index_or_indices = sub_expr1, summand = al, domain = S), Sum(index_or_indices = sub_expr1, summand = bl, domain = S)))))

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, S\right) \mapsto \left(\left[\forall_{k \in S}~\left(a\left(k\right) \leq b\left(k\right)\right)\right] \Rightarrow \left(\left[\sum_{l \in S}~a\left(l\right)\right] \leq \left[\sum_{l \in S}~b\left(l\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	33, 34, 40
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 22 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 13
11	Lambda	parameter: 38 body: 14
12	Operation	operator: 16 operand: 20
13	Operation	operator: 16 operand: 21
14	Conditional	value: 18 condition: 19
15	ExprTuple	20
16	Literal
17	ExprTuple	21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 36 operands: 24
20	Lambda	parameter: 39 body: 25
21	Lambda	parameter: 39 body: 26
22	Literal
23	ExprTuple	27, 28
24	ExprTuple	38, 40
25	Conditional	value: 29 condition: 31
26	Conditional	value: 30 condition: 31
27	Operation	operator: 33 operand: 38
28	Operation	operator: 34 operand: 38
29	Operation	operator: 33 operand: 39
30	Operation	operator: 34 operand: 39
31	Operation	operator: 36 operands: 37
32	ExprTuple	38
33	Variable
34	Variable
35	ExprTuple	39
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Variable
40	Variable