logo

Expression of type Conditional

from the theory of proveit.logic.booleans.disjunction

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 C, Conditional, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, D_1_to_n
from proveit.logic import And, Boolean, Equals, Forall, InSet, Or
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C, D_1_to_n], instance_expr = Equals(Or(A_1_to_l, B_1_to_m, C, D_1_to_n), Or(A_1_to_l, C, B_1_to_m, D_1_to_n)).with_wrapping_at(2), domain = Boolean), And(InSet(l, Natural), InSet(m, Natural), InSet(n, 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_{l}, B_{1}, B_{2}, \ldots, B_{m}, C, D_{1}, D_{2}, \ldots, D_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m} \lor C\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}\right) =  \\ \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor C\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}\right) \end{array} \end{array}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  n \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: 50
operands: 11
8Operationoperator: 50
operands: 12
9Operationoperator: 50
operands: 13
10Conditionalvalue: 14
condition: 15
11ExprTuple42, 16
12ExprTuple44, 16
13ExprTuple47, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Literal
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple23, 24, 25, 26
21Operationoperator: 28
operands: 27
22Operationoperator: 28
operands: 29
23ExprRangelambda_map: 30
start_index: 46
end_index: 42
24ExprRangelambda_map: 31
start_index: 46
end_index: 44
25Operationoperator: 50
operands: 32
26ExprRangelambda_map: 33
start_index: 46
end_index: 47
27ExprTuple34, 35, 39, 36
28Literal
29ExprTuple34, 39, 35, 36
30Lambdaparameter: 60
body: 37
31Lambdaparameter: 60
body: 38
32ExprTuple39, 55
33Lambdaparameter: 60
body: 40
34ExprRangelambda_map: 41
start_index: 46
end_index: 42
35ExprRangelambda_map: 43
start_index: 46
end_index: 44
36ExprRangelambda_map: 45
start_index: 46
end_index: 47
37Operationoperator: 50
operands: 48
38Operationoperator: 50
operands: 49
39Variable
40Operationoperator: 50
operands: 51
41Lambdaparameter: 60
body: 52
42Variable
43Lambdaparameter: 60
body: 53
44Variable
45Lambdaparameter: 60
body: 54
46Literal
47Variable
48ExprTuple52, 55
49ExprTuple53, 55
50Literal
51ExprTuple54, 55
52IndexedVarvariable: 56
index: 60
53IndexedVarvariable: 57
index: 60
54IndexedVarvariable: 58
index: 60
55Literal
56Variable
57Variable
58Variable
59ExprTuple60
60Variable