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, Function, R, S, a, f, fa, fx, gy, n, x, y
from proveit.logic import And, Card, Equals, Forall, Implies, InSet, SetOfAll
from proveit.numbers import Complex, Sum

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = Conditional(Implies(Forall(instance_param_or_params = [a], instance_expr = InSet(fa, Complex), domain = R), Equals(Sum(index_or_indices = [x], summand = fx, domain = R), Sum(index_or_indices = sub_expr1, summand = Function(f, [gy]), domain = S))), And(Equals(SetOfAll(instance_param_or_params = sub_expr1, instance_element = gy, domain = S), R), Equals(Card(S), n), Equals(Card(R), n)))

# 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[\forall_{a \in R}~\left(f\left(a\right) \in \mathbb{C}\right)\right] \Rightarrow \left(\left[\sum_{x \in R}~f\left(x\right)\right] = \left[\sum_{y \in S}~f\left(g\left(y\right)\right)\right]\right) \textrm{ if } \left\{g\left(y\right)\right\}_{y \in S} = R ,  |S| = n ,  |R| = n\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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 12 operand: 19
8	Operation	operator: 17 operands: 14
9	Operation	operator: 17 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19
14	ExprTuple	20, 21
15	ExprTuple	22, 60
16	ExprTuple	23, 25
17	Literal
18	ExprTuple	24, 25
19	Lambda	parameter: 58 body: 26
20	Operation	operator: 28 operand: 37
21	Operation	operator: 28 operand: 38
22	Operation	operator: 30 operand: 39
23	Operation	operator: 33 operand: 62
24	Operation	operator: 33 operand: 60
25	Variable
26	Conditional	value: 35 condition: 36
27	ExprTuple	37
28	Literal
29	ExprTuple	38
30	Literal
31	ExprTuple	39
32	ExprTuple	62
33	Literal
34	ExprTuple	60
35	Operation	operator: 56 operands: 40
36	Operation	operator: 56 operands: 41
37	Lambda	parameter: 59 body: 42
38	Lambda	parameter: 65 body: 43
39	Lambda	parameter: 65 body: 44
40	ExprTuple	45, 46
41	ExprTuple	58, 60
42	Conditional	value: 47 condition: 48
43	Conditional	value: 49 condition: 50
44	Conditional	value: 61 condition: 50
45	Operation	operator: 54 operand: 58
46	Literal
47	Operation	operator: 54 operand: 59
48	Operation	operator: 56 operands: 53
49	Operation	operator: 54 operand: 61
50	Operation	operator: 56 operands: 57
51	ExprTuple	58
52	ExprTuple	59
53	ExprTuple	59, 60
54	Variable
55	ExprTuple	61
56	Literal
57	ExprTuple	65, 62
58	Variable
59	Variable
60	Variable
61	Operation	operator: 63 operand: 65
62	Variable
63	Variable
64	ExprTuple	65
65	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶