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, fa, fx, x
from proveit.logic import And, InSet, SubsetEq
from proveit.numbers import Add, Integer, Integrate, Interval, IntervalCC, LessEq, Sum

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = IntervalCC(a, b)
expr = ExprTuple(Lambda([a, b], Conditional(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))), And(InSet(a, Integer), InSet(b, Integer), LessEq(a, b), SubsetEq(sub_expr2, 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(a, b\right) \mapsto \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) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a \leq b ,  \left[a,b\right] \subseteq S\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: 47 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 20 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12, 13
8	Operation	operator: 14 operand: 23
9	Operation	operator: 16 operands: 17
10	Operation	operator: 42 operands: 18
11	Operation	operator: 42 operands: 19
12	Operation	operator: 20 operands: 47
13	Operation	operator: 21 operands: 22
14	Literal
15	ExprTuple	23
16	Literal
17	ExprTuple	24, 25
18	ExprTuple	48, 26
19	ExprTuple	49, 26
20	Literal
21	Literal
22	ExprTuple	45, 27
23	Lambda	parameter: 44 body: 28
24	Operation	operator: 40 operand: 48
25	Operation	operator: 30 operand: 33
26	Literal
27	Variable
28	Conditional	value: 37 condition: 32
29	ExprTuple	48
30	Literal
31	ExprTuple	33
32	Operation	operator: 42 operands: 34
33	Lambda	parameter: 44 body: 35
34	ExprTuple	44, 36
35	Conditional	value: 37 condition: 38
36	Operation	operator: 39 operands: 47
37	Operation	operator: 40 operand: 44
38	Operation	operator: 42 operands: 43
39	Literal
40	Variable
41	ExprTuple	44
42	Literal
43	ExprTuple	44, 45
44	Variable
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Variable