Expression of type Conditional

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, S, 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 = 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[\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 26 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	8, 9
6	Operation	operator: 10 operand: 15
7	Operation	operator: 26 operands: 12
8	Literal
9	Operation	operator: 13 operand: 44
10	Literal
11	ExprTuple	15
12	ExprTuple	16, 17
13	Literal
14	ExprTuple	44
15	Lambda	parameter: 42 body: 18
16	Operation	operator: 20 operand: 24
17	Operation	operator: 20 operand: 25
18	Conditional	value: 22 condition: 23
19	ExprTuple	24
20	Literal
21	ExprTuple	25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 40 operands: 28
24	Lambda	parameter: 43 body: 29
25	Lambda	parameter: 43 body: 30
26	Literal
27	ExprTuple	31, 32
28	ExprTuple	42, 44
29	Conditional	value: 33 condition: 35
30	Conditional	value: 34 condition: 35
31	Operation	operator: 37 operand: 42
32	Operation	operator: 38 operand: 42
33	Operation	operator: 37 operand: 43
34	Operation	operator: 38 operand: 43
35	Operation	operator: 40 operands: 41
36	ExprTuple	42
37	Variable
38	Variable
39	ExprTuple	43
40	Literal
41	ExprTuple	43, 44
42	Variable
43	Variable
44	Variable