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, c, d, fj, gj, j, x
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Integer, Interval, Mult, Sum

# build up the expression from sub-expressions
sub_expr1 = [j]
sub_expr2 = Interval(c, d)
expr = Conditional(Forall(instance_param_or_params = [c, d], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(Mult(x, gj), fj), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = Mult(gj, fj), domain = sub_expr2))), domain = Integer), InSet(x, Complex))

# 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_{c, d \in \mathbb{Z}}~\left(\left(\sum_{j = c}^{d} \left(\left(x \cdot g\left(j\right)\right) \cdot f\left(j\right)\right)\right) = \left(x \cdot \left(\sum_{j = c}^{d} \left(g\left(j\right) \cdot f\left(j\right)\right)\right)\right)\right) \textrm{ if } x \in \mathbb{C}\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: 6
2	Operation	operator: 39 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	41, 7
6	Lambda	parameters: 49 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 27 operand: 23
16	Operation	operator: 37 operands: 20
17	Operation	operator: 39 operands: 21
18	Operation	operator: 39 operands: 22
19	ExprTuple	23
20	ExprTuple	41, 24
21	ExprTuple	51, 25
22	ExprTuple	52, 25
23	Lambda	parameter: 50 body: 26
24	Operation	operator: 27 operand: 30
25	Literal
26	Conditional	value: 29 condition: 35
27	Literal
28	ExprTuple	30
29	Operation	operator: 37 operands: 31
30	Lambda	parameter: 50 body: 32
31	ExprTuple	33, 43
32	Conditional	value: 34 condition: 35
33	Operation	operator: 37 operands: 36
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 40
36	ExprTuple	41, 42
37	Literal
38	ExprTuple	42, 43
39	Literal
40	ExprTuple	50, 44
41	Variable
42	Operation	operator: 45 operand: 50
43	Operation	operator: 46 operand: 50
44	Operation	operator: 48 operands: 49
45	Variable
46	Variable
47	ExprTuple	50
48	Literal
49	ExprTuple	51, 52
50	Variable
51	Variable
52	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶