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, f, fx, g, gx, x
from proveit.logic import Forall, Implies
from proveit.numbers import LessEq, Sum

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Lambda([S, f, g], Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = LessEq(fx, gx), domain = S), LessEq(Sum(index_or_indices = sub_expr1, summand = fx, domain = S), Sum(index_or_indices = sub_expr1, summand = gx, 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(S, f, g\right) \mapsto \left(\left[\forall_{x \in S}~\left(f\left(x\right) \leq g\left(x\right)\right)\right] \Rightarrow \left(\left[\sum_{x \in S}~f\left(x\right)\right] \leq \left[\sum_{x \in S}~g\left(x\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	33, 27, 28
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 20 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameter: 32 body: 13
11	Operation	operator: 15 operand: 18
12	Operation	operator: 15 operand: 19
13	Conditional	value: 17 condition: 26
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Lambda	parameter: 32 body: 22
19	Lambda	parameter: 32 body: 23
20	Literal
21	ExprTuple	24, 25
22	Conditional	value: 24 condition: 26
23	Conditional	value: 25 condition: 26
24	Operation	operator: 27 operand: 32
25	Operation	operator: 28 operand: 32
26	Operation	operator: 30 operands: 31
27	Variable
28	Variable
29	ExprTuple	32
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Variable