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, a, b, i, x
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Integer, Interval, Mult, Neg, Sum, one

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Sum(index_or_indices = [i], summand = x, domain = Interval(a, b)), Mult(Add(b, Neg(a), one), x)), domain = Complex), And(InSet(a, Integer), InSet(b, Integer)))

# 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\{\forall_{x \in \mathbb{C}}~\left(\left(\sum_{i = a}^{b} x\right) = \left(\left(b - a + 1\right) \cdot x\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 33 body: 11
8	Operation	operator: 37 operands: 12
9	Operation	operator: 37 operands: 13
10	ExprTuple	33
11	Conditional	value: 14 condition: 15
12	ExprTuple	45, 16
13	ExprTuple	46, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 37 operands: 19
16	Literal
17	Literal
18	ExprTuple	20, 21
19	ExprTuple	33, 22
20	Operation	operator: 23 operand: 27
21	Operation	operator: 25 operands: 26
22	Literal
23	Literal
24	ExprTuple	27
25	Literal
26	ExprTuple	28, 33
27	Lambda	parameter: 41 body: 30
28	Operation	operator: 31 operands: 32
29	ExprTuple	41
30	Conditional	value: 33 condition: 34
31	Literal
32	ExprTuple	46, 35, 36
33	Variable
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operand: 45
36	Literal
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	45
41	Variable
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶