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 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 = 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(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)

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