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, g, gy, n, x, y
from proveit.logic import Card, Equals, Forall, Implies, InSet, SetOfAll
from proveit.numbers import Complex, Natural, Sum

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = Conditional(Forall(instance_param_or_params = [f, g, R, S], instance_expr = 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))), conditions = [Equals(SetOfAll(instance_param_or_params = sub_expr1, instance_element = gy, domain = S), R), Equals(Card(S), n), Equals(Card(R), n)]), InSet(n, Natural))

# 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_{f, g, R, S~|~\left\{g\left(y\right)\right\}_{y \in S} = R, |S| = n, |R| = n}~\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)\right) \textrm{ if } n \in \mathbb{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: 20 operand: 5
2	Operation	operator: 64 operands: 4
3	ExprTuple	5
4	ExprTuple	33, 6
5	Lambda	parameters: 7 body: 8
6	Literal
7	ExprTuple	62, 71, 68, 70
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, 19
15	Operation	operator: 20 operand: 27
16	Operation	operator: 25 operands: 22
17	Operation	operator: 25 operands: 23
18	Operation	operator: 25 operands: 24
19	Operation	operator: 25 operands: 26
20	Literal
21	ExprTuple	27
22	ExprTuple	28, 29
23	ExprTuple	30, 68
24	ExprTuple	31, 33
25	Literal
26	ExprTuple	32, 33
27	Lambda	parameter: 66 body: 34
28	Operation	operator: 36 operand: 45
29	Operation	operator: 36 operand: 46
30	Operation	operator: 38 operand: 47
31	Operation	operator: 41 operand: 70
32	Operation	operator: 41 operand: 68
33	Variable
34	Conditional	value: 43 condition: 44
35	ExprTuple	45
36	Literal
37	ExprTuple	46
38	Literal
39	ExprTuple	47
40	ExprTuple	70
41	Literal
42	ExprTuple	68
43	Operation	operator: 64 operands: 48
44	Operation	operator: 64 operands: 49
45	Lambda	parameter: 67 body: 50
46	Lambda	parameter: 73 body: 51
47	Lambda	parameter: 73 body: 52
48	ExprTuple	53, 54
49	ExprTuple	66, 68
50	Conditional	value: 55 condition: 56
51	Conditional	value: 57 condition: 58
52	Conditional	value: 69 condition: 58
53	Operation	operator: 62 operand: 66
54	Literal
55	Operation	operator: 62 operand: 67
56	Operation	operator: 64 operands: 61
57	Operation	operator: 62 operand: 69
58	Operation	operator: 64 operands: 65
59	ExprTuple	66
60	ExprTuple	67
61	ExprTuple	67, 68
62	Variable
63	ExprTuple	69
64	Literal
65	ExprTuple	73, 70
66	Variable
67	Variable
68	Variable
69	Operation	operator: 71 operand: 73
70	Variable
71	Variable
72	ExprTuple	73
73	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶