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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 Conditional, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_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_1_to_n], instance_expr = Equals(Or(A_1_to_l, B_1_to_m, C_1_to_n), Or(A_1_to_l, Or(B_1_to_m), C_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_{1}, C_{2}, \ldots, C_{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_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) =  \\ \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor \left(B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\right)\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{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: 26
body: 10
7Operationoperator: 45
operands: 11
8Operationoperator: 45
operands: 12
9Operationoperator: 45
operands: 13
10Conditionalvalue: 14
condition: 15
11ExprTuple38, 16
12ExprTuple53, 16
13ExprTuple42, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Literal
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple23, 24, 25
21Operationoperator: 39
operands: 26
22Operationoperator: 39
operands: 27
23ExprRangelambda_map: 28
start_index: 52
end_index: 38
24ExprRangelambda_map: 29
start_index: 52
end_index: 53
25ExprRangelambda_map: 30
start_index: 52
end_index: 42
26ExprTuple31, 47, 33
27ExprTuple31, 32, 33
28Lambdaparameter: 59
body: 34
29Lambdaparameter: 59
body: 35
30Lambdaparameter: 59
body: 36
31ExprRangelambda_map: 37
start_index: 52
end_index: 38
32Operationoperator: 39
operands: 40
33ExprRangelambda_map: 41
start_index: 52
end_index: 42
34Operationoperator: 45
operands: 43
35Operationoperator: 45
operands: 44
36Operationoperator: 45
operands: 46
37Lambdaparameter: 59
body: 48
38Variable
39Literal
40ExprTuple47
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