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, a, b, f, fa, fx, x
from proveit.logic import Forall, 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(S, Forall(instance_param_or_params = [f], instance_expr = 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)]), domain = MonDecFuncs(S), condition = 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(S \mapsto \left[\forall_{f \in \textrm{MonDecFuncs}\left(S\right)~|~S \subseteq \mathbb{R}}~\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)\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	parameter: 46 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 59 body: 6
5	ExprTuple	59
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 23 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 14
12	Lambda	parameters: 66 body: 15
13	Operation	operator: 61 operands: 16
14	Operation	operator: 40 operands: 17
15	Conditional	value: 18 condition: 19
16	ExprTuple	59, 20
17	ExprTuple	46, 21
18	Operation	operator: 39 operands: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operand: 46
21	Literal
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29, 30, 31, 32
25	Literal
26	ExprTuple	46
27	Operation	operator: 33 operand: 42
28	Operation	operator: 35 operands: 36
29	Operation	operator: 61 operands: 37
30	Operation	operator: 61 operands: 38
31	Operation	operator: 39 operands: 66
32	Operation	operator: 40 operands: 41
33	Literal
34	ExprTuple	42
35	Literal
36	ExprTuple	43, 44
37	ExprTuple	67, 45
38	ExprTuple	68, 45
39	Literal
40	Literal
41	ExprTuple	64, 46
42	Lambda	parameter: 63 body: 47
43	Operation	operator: 59 operand: 67
44	Operation	operator: 49 operand: 52
45	Literal
46	Variable
47	Conditional	value: 56 condition: 51
48	ExprTuple	67
49	Literal
50	ExprTuple	52
51	Operation	operator: 61 operands: 53
52	Lambda	parameter: 63 body: 54
53	ExprTuple	63, 55
54	Conditional	value: 56 condition: 57
55	Operation	operator: 58 operands: 66
56	Operation	operator: 59 operand: 63
57	Operation	operator: 61 operands: 62
58	Literal
59	Variable
60	ExprTuple	63
61	Literal
62	ExprTuple	63, 64
63	Variable
64	Operation	operator: 65 operands: 66
65	Literal
66	ExprTuple	67, 68
67	Variable
68	Variable