Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	39, 40, 46
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 28 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 11
8	Operation	operator: 12 operand: 17
9	Operation	operator: 28 operands: 14
10	Literal
11	Operation	operator: 15 operand: 46
12	Literal
13	ExprTuple	17
14	ExprTuple	18, 19
15	Literal
16	ExprTuple	46
17	Lambda	parameter: 44 body: 20
18	Operation	operator: 22 operand: 26
19	Operation	operator: 22 operand: 27
20	Conditional	value: 24 condition: 25
21	ExprTuple	26
22	Literal
23	ExprTuple	27
24	Operation	operator: 28 operands: 29
25	Operation	operator: 42 operands: 30
26	Lambda	parameter: 45 body: 31
27	Lambda	parameter: 45 body: 32
28	Literal
29	ExprTuple	33, 34
30	ExprTuple	44, 46
31	Conditional	value: 35 condition: 37
32	Conditional	value: 36 condition: 37
33	Operation	operator: 39 operand: 44
34	Operation	operator: 40 operand: 44
35	Operation	operator: 39 operand: 45
36	Operation	operator: 40 operand: 45
37	Operation	operator: 42 operands: 43
38	ExprTuple	44
39	Variable
40	Variable
41	ExprTuple	45
42	Literal
43	ExprTuple	45, 46
44	Variable
45	Variable
46	Variable