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

# build up the expression from sub-expressions
sub_expr1 = [x]
sub_expr2 = IntervalCC(subtract(a, one), b)
expr = ExprTuple(Lambda([a, b], Conditional(LessEq(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), 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(\int_{a - 1}^{b} f\left(x\right)\,dx\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a \leq b ,  \left[a - 1,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: 41 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 operand: 24
10	Operation	operator: 35 operands: 18
11	Operation	operator: 35 operands: 19
12	Operation	operator: 20 operands: 41
13	Operation	operator: 21 operands: 22
14	Literal
15	ExprTuple	23
16	Literal
17	ExprTuple	24
18	ExprTuple	48, 25
19	ExprTuple	45, 25
20	Literal
21	Literal
22	ExprTuple	39, 26
23	Lambda	parameter: 38 body: 27
24	Lambda	parameter: 38 body: 28
25	Literal
26	Variable
27	Conditional	value: 30 condition: 29
28	Conditional	value: 30 condition: 31
29	Operation	operator: 35 operands: 32
30	Operation	operator: 33 operand: 38
31	Operation	operator: 35 operands: 36
32	ExprTuple	38, 37
33	Variable
34	ExprTuple	38
35	Literal
36	ExprTuple	38, 39
37	Operation	operator: 40 operands: 41
38	Variable
39	Operation	operator: 42 operands: 43
40	Literal
41	ExprTuple	48, 45
42	Literal
43	ExprTuple	44, 45
44	Operation	operator: 46 operands: 47
45	Variable
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Operation	operator: 50 operand: 52
50	Literal
51	ExprTuple	52
52	Literal