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, 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 = 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)))

# 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(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..

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 operands: 15
8	Operation	operator: 40 operands: 16
9	Operation	operator: 40 operands: 17
10	Operation	operator: 18 operands: 45
11	Operation	operator: 19 operands: 20
12	Literal
13	ExprTuple	21
14	Literal
15	ExprTuple	22, 23
16	ExprTuple	46, 24
17	ExprTuple	47, 24
18	Literal
19	Literal
20	ExprTuple	43, 25
21	Lambda	parameter: 42 body: 26
22	Operation	operator: 38 operand: 46
23	Operation	operator: 28 operand: 31
24	Literal
25	Variable
26	Conditional	value: 35 condition: 30
27	ExprTuple	46
28	Literal
29	ExprTuple	31
30	Operation	operator: 40 operands: 32
31	Lambda	parameter: 42 body: 33
32	ExprTuple	42, 34
33	Conditional	value: 35 condition: 36
34	Operation	operator: 37 operands: 45
35	Operation	operator: 38 operand: 42
36	Operation	operator: 40 operands: 41
37	Literal
38	Variable
39	ExprTuple	42
40	Literal
41	ExprTuple	42, 43
42	Variable
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶