Expression of type Conditional ¶

from the theory of proveit.numbers.addition.subtraction ¶

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, b, d, i, j, k
from proveit.core_expr_types import a_1_to_i, c_1_to_j, e_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural, Neg

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j, d, e_1_to_k], instance_expr = Equals(Add(a_1_to_i, Neg(b), c_1_to_j, d, e_1_to_k), Add(a_1_to_i, c_1_to_j, e_1_to_k)), domain = Complex), And(InSet(i, Natural), InSet(j, Natural), InSet(k, 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_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}, d, e_{1}, e_{2}, \ldots, e_{k} \in \mathbb{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} - b+ c_{1} +  c_{2} +  \ldots +  c_{j} + d+ e_{1} +  e_{2} +  \ldots +  e_{k}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ c_{1} +  c_{2} +  \ldots +  c_{j}+ e_{1} +  e_{2} +  \ldots +  e_{k}\right)\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \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: 3 operand: 6
2	Operation	operator: 20 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 10 body: 11
7	Operation	operator: 56 operands: 12
8	Operation	operator: 56 operands: 13
9	Operation	operator: 56 operands: 14
10	ExprTuple	38, 58, 39, 43, 40
11	Conditional	value: 15 condition: 16
12	ExprTuple	48, 17
13	ExprTuple	50, 17
14	ExprTuple	53, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26, 27, 28
22	Operation	operator: 30 operands: 29
23	Operation	operator: 30 operands: 31
24	ExprRange	lambda_map: 32 start_index: 52 end_index: 48
25	Operation	operator: 56 operands: 33
26	ExprRange	lambda_map: 34 start_index: 52 end_index: 50
27	Operation	operator: 56 operands: 35
28	ExprRange	lambda_map: 36 start_index: 52 end_index: 53
29	ExprTuple	38, 37, 39, 43, 40
30	Literal
31	ExprTuple	38, 39, 40
32	Lambda	parameter: 67 body: 41
33	ExprTuple	58, 62
34	Lambda	parameter: 67 body: 42
35	ExprTuple	43, 62
36	Lambda	parameter: 67 body: 44
37	Operation	operator: 45 operand: 58
38	ExprRange	lambda_map: 47 start_index: 52 end_index: 48
39	ExprRange	lambda_map: 49 start_index: 52 end_index: 50
40	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
41	Operation	operator: 56 operands: 54
42	Operation	operator: 56 operands: 55
43	Variable
44	Operation	operator: 56 operands: 57
45	Literal
46	ExprTuple	58
47	Lambda	parameter: 67 body: 59
48	Variable
49	Lambda	parameter: 67 body: 60
50	Variable
51	Lambda	parameter: 67 body: 61
52	Literal
53	Variable
54	ExprTuple	59, 62
55	ExprTuple	60, 62
56	Literal
57	ExprTuple	61, 62
58	Variable
59	IndexedVar	variable: 63 index: 67
60	IndexedVar	variable: 64 index: 67
61	IndexedVar	variable: 65 index: 67
62	Literal
63	Variable
64	Variable
65	Variable
66	ExprTuple	67
67	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.addition.subtraction¶

Expression of type Conditional ¶

from the theory of proveit.numbers.addition.subtraction ¶