Expression of type Conditional ¶

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, 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 = 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)))

# 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(\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..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 18 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10, 11
6	Operation	operator: 12 operand: 21
7	Operation	operator: 14 operand: 22
8	Operation	operator: 33 operands: 16
9	Operation	operator: 33 operands: 17
10	Operation	operator: 18 operands: 39
11	Operation	operator: 19 operands: 20
12	Literal
13	ExprTuple	21
14	Literal
15	ExprTuple	22
16	ExprTuple	46, 23
17	ExprTuple	43, 23
18	Literal
19	Literal
20	ExprTuple	37, 24
21	Lambda	parameter: 36 body: 25
22	Lambda	parameter: 36 body: 26
23	Literal
24	Variable
25	Conditional	value: 28 condition: 27
26	Conditional	value: 28 condition: 29
27	Operation	operator: 33 operands: 30
28	Operation	operator: 31 operand: 36
29	Operation	operator: 33 operands: 34
30	ExprTuple	36, 35
31	Variable
32	ExprTuple	36
33	Literal
34	ExprTuple	36, 37
35	Operation	operator: 38 operands: 39
36	Variable
37	Operation	operator: 40 operands: 41
38	Literal
39	ExprTuple	46, 43
40	Literal
41	ExprTuple	42, 43
42	Operation	operator: 44 operands: 45
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Operation	operator: 48 operand: 50
48	Literal
49	ExprTuple	50
50	Literal

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶