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Expression of type ExprTuple

from the theory of proveit.numbers.addition

In [1]:
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, ExprTuple, Lambda, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = Equals(Add(a_1_to_i, Add(b_1_to_j), c_1_to_k), Add(a_1_to_i, b_1_to_j, c_1_to_k)).with_wrapping_at(2), domain = Complex), And(InSet(i, Natural), InSet(j, Natural), InSet(k, Natural)))))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left(i, j, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k} \in \mathbb{C}}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i} + \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}+ c_{1} +  c_{2} +  \ldots +  c_{k}\right) \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  k \in \mathbb{N}\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple43, 56, 45
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 22
operands: 8
6Literal
7ExprTuple9
8ExprTuple10, 11, 12
9Lambdaparameters: 30
body: 13
10Operationoperator: 48
operands: 14
11Operationoperator: 48
operands: 15
12Operationoperator: 48
operands: 16
13Conditionalvalue: 17
condition: 18
14ExprTuple43, 19
15ExprTuple56, 19
16ExprTuple45, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple24, 25
22Literal
23ExprTuple26, 27, 28
24Operationoperator: 40
operands: 29
25Operationoperator: 40
operands: 30
26ExprRangelambda_map: 31
start_index: 55
end_index: 43
27ExprRangelambda_map: 32
start_index: 55
end_index: 56
28ExprRangelambda_map: 33
start_index: 55
end_index: 45
29ExprTuple35, 34, 36
30ExprTuple35, 50, 36
31Lambdaparameter: 62
body: 37
32Lambdaparameter: 62
body: 38
33Lambdaparameter: 62
body: 39
34Operationoperator: 40
operands: 41
35ExprRangelambda_map: 42
start_index: 55
end_index: 43
36ExprRangelambda_map: 44
start_index: 55
end_index: 45
37Operationoperator: 48
operands: 46
38Operationoperator: 48
operands: 47
39Operationoperator: 48
operands: 49
40Literal
41ExprTuple50
42Lambdaparameter: 62
body: 51
43Variable
44Lambdaparameter: 62
body: 52
45Variable
46ExprTuple51, 53
47ExprTuple59, 53
48Literal
49ExprTuple52, 53
50ExprRangelambda_map: 54
start_index: 55
end_index: 56
51IndexedVarvariable: 57
index: 62
52IndexedVarvariable: 58
index: 62
53Literal
54Lambdaparameter: 62
body: 59
55Literal
56Variable
57Variable
58Variable
59IndexedVarvariable: 60
index: 62
60Variable
61ExprTuple62
62Variable