Expression of type Conditional¶

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.
# import Expression classes needed to build the expression
from proveit import Conditional, 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 = 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\{\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..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 19
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 8, 9
6Lambdaparameters: 27
body: 10
7Operationoperator: 45
operands: 11
8Operationoperator: 45
operands: 12
9Operationoperator: 45
operands: 13
10Conditionalvalue: 14
condition: 15
11ExprTuple40, 16
12ExprTuple53, 16
13ExprTuple42, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Literal
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple23, 24, 25
21Operationoperator: 37
operands: 26
22Operationoperator: 37
operands: 27
23ExprRangelambda_map: 28
start_index: 52
end_index: 40
24ExprRangelambda_map: 29
start_index: 52
end_index: 53
25ExprRangelambda_map: 30
start_index: 52
end_index: 42
26ExprTuple32, 31, 33
27ExprTuple32, 47, 33
28Lambdaparameter: 59
body: 34
29Lambdaparameter: 59
body: 35
30Lambdaparameter: 59
body: 36
31Operationoperator: 37
operands: 38
32ExprRangelambda_map: 39
start_index: 52
end_index: 40
33ExprRangelambda_map: 41
start_index: 52
end_index: 42
34Operationoperator: 45
operands: 43
35Operationoperator: 45
operands: 44
36Operationoperator: 45
operands: 46
37Literal
38ExprTuple47
39Lambdaparameter: 59
body: 48
40Variable
41Lambdaparameter: 59
body: 49
42Variable
43ExprTuple48, 50
44ExprTuple56, 50
45Literal
46ExprTuple49, 50
47ExprRangelambda_map: 51
start_index: 52
end_index: 53
48IndexedVarvariable: 54
index: 59
49IndexedVarvariable: 55
index: 59
50Literal
51Lambdaparameter: 59
body: 56
52Literal
53Variable
54Variable
55Variable
56IndexedVarvariable: 57
index: 59
57Variable
58ExprTuple59
59Variable