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