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 Conditional, ExprTuple, Lambda, S, a, b, f, fa, fx, x
from proveit.logic import And, Forall, InSet, SubsetEq
from proveit.numbers import Add, Integer, Integrate, Interval, IntervalCC, LessEq, MonDecFuncs, Real, Sum

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = IntervalCC(a, b)
expr = ExprTuple(Lambda(f, Conditional(Forall(instance_param_or_params = [a, b], instance_expr = LessEq(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Add(fa, Integrate(index_or_indices = sub_expr1, integrand = fx, domain = sub_expr2))), domain = Integer, conditions = [LessEq(a, b), SubsetEq(sub_expr2, S)]), And(InSet(f, MonDecFuncs(S)), SubsetEq(S, Real)))))

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(f \mapsto \left\{\forall_{a, b \in \mathbb{Z}~|~a \leq b, \left[a,b\right] \subseteq S}~\left(\left(\sum_{x = a}^{b} f\left(x\right)\right) \leq \left(f\left(a\right) + \left(\int_{a}^{b} f\left(x\right)\,dx\right)\right)\right) \textrm{ if } f \in \textrm{MonDecFuncs}\left(S\right) ,  S \subseteq \mathbb{R}\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	parameter: 56 body: 3
2	ExprTuple	56
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 63 body: 12
10	Operation	operator: 58 operands: 13
11	Operation	operator: 37 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	56, 17
14	ExprTuple	43, 18
15	Operation	operator: 36 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operand: 43
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	26, 27, 28, 29
22	Literal
23	ExprTuple	43
24	Operation	operator: 30 operand: 39
25	Operation	operator: 32 operands: 33
26	Operation	operator: 58 operands: 34
27	Operation	operator: 58 operands: 35
28	Operation	operator: 36 operands: 63
29	Operation	operator: 37 operands: 38
30	Literal
31	ExprTuple	39
32	Literal
33	ExprTuple	40, 41
34	ExprTuple	64, 42
35	ExprTuple	65, 42
36	Literal
37	Literal
38	ExprTuple	61, 43
39	Lambda	parameter: 60 body: 44
40	Operation	operator: 56 operand: 64
41	Operation	operator: 46 operand: 49
42	Literal
43	Variable
44	Conditional	value: 53 condition: 48
45	ExprTuple	64
46	Literal
47	ExprTuple	49
48	Operation	operator: 58 operands: 50
49	Lambda	parameter: 60 body: 51
50	ExprTuple	60, 52
51	Conditional	value: 53 condition: 54
52	Operation	operator: 55 operands: 63
53	Operation	operator: 56 operand: 60
54	Operation	operator: 58 operands: 59
55	Literal
56	Variable
57	ExprTuple	60
58	Literal
59	ExprTuple	60, 61
60	Variable
61	Operation	operator: 62 operands: 63
62	Literal
63	ExprTuple	64, 65
64	Variable
65	Variable