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, S, a, b, k, l
from proveit.logic import Card, Forall, Implies
from proveit.numbers import Less, Sum, greater, zero
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], Conditional(Implies(Forall(instance_param_or_params = [k], instance_expr = Less(ak, bk), domain = S), Less(Sum(index_or_indices = sub_expr1, summand = al, domain = S), Sum(index_or_indices = sub_expr1, summand = bl, domain = S))), greater(Card(S), zero))))

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) < b\left(k\right)\right)\right] \Rightarrow \left(\left[\sum_{l \in S}~a\left(l\right)\right] < \left[\sum_{l \in S}~b\left(l\right)\right]\right) \textrm{ if } |S| > 0\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	40, 41, 47
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 29 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	11, 12
9	Operation	operator: 13 operand: 18
10	Operation	operator: 29 operands: 15
11	Literal
12	Operation	operator: 16 operand: 47
13	Literal
14	ExprTuple	18
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	47
18	Lambda	parameter: 45 body: 21
19	Operation	operator: 23 operand: 27
20	Operation	operator: 23 operand: 28
21	Conditional	value: 25 condition: 26
22	ExprTuple	27
23	Literal
24	ExprTuple	28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 43 operands: 31
27	Lambda	parameter: 46 body: 32
28	Lambda	parameter: 46 body: 33
29	Literal
30	ExprTuple	34, 35
31	ExprTuple	45, 47
32	Conditional	value: 36 condition: 38
33	Conditional	value: 37 condition: 38
34	Operation	operator: 40 operand: 45
35	Operation	operator: 41 operand: 45
36	Operation	operator: 40 operand: 46
37	Operation	operator: 41 operand: 46
38	Operation	operator: 43 operands: 44
39	ExprTuple	45
40	Variable
41	Variable
42	ExprTuple	46
43	Literal
44	ExprTuple	46, 47
45	Variable
46	Variable
47	Variable