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Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

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 B, Conditional, l, m, n
from proveit.core_expr_types import A_1_to_l, C_1_to_m, D_1_to_n
from proveit.logic import And, Boolean, Equals, Forall, InSet
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, C_1_to_m, D_1_to_n], instance_expr = Equals(And(A_1_to_l, B, C_1_to_m, D_1_to_n), And(A_1_to_l, C_1_to_m, B, 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, C_{1}, C_{2}, \ldots, C_{m}, D_{1}, D_{2}, \ldots, D_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land B\land C_{1} \land  C_{2} \land  \ldots \land  C_{m}\land D_{1} \land  D_{2} \land  \ldots \land  D_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land C_{1} \land  C_{2} \land  \ldots \land  C_{m} \land B\land D_{1} \land  D_{2} \land  \ldots \land  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: 27
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 8, 9
6Lambdaparameters: 26
body: 10
7Operationoperator: 49
operands: 11
8Operationoperator: 49
operands: 12
9Operationoperator: 49
operands: 13
10Conditionalvalue: 14
condition: 15
11ExprTuple41, 16
12ExprTuple43, 16
13ExprTuple46, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 27
operands: 19
16Literal
17Literal
18ExprTuple20, 21
19ExprTuple22, 23, 24, 25
20Operationoperator: 27
operands: 26
21Operationoperator: 27
operands: 28
22ExprRangelambda_map: 29
start_index: 45
end_index: 41
23Operationoperator: 49
operands: 30
24ExprRangelambda_map: 31
start_index: 45
end_index: 43
25ExprRangelambda_map: 32
start_index: 45
end_index: 46
26ExprTuple33, 37, 34, 35
27Literal
28ExprTuple33, 34, 37, 35
29Lambdaparameter: 59
body: 36
30ExprTuple37, 54
31Lambdaparameter: 59
body: 38
32Lambdaparameter: 59
body: 39
33ExprRangelambda_map: 40
start_index: 45
end_index: 41
34ExprRangelambda_map: 42
start_index: 45
end_index: 43
35ExprRangelambda_map: 44
start_index: 45
end_index: 46
36Operationoperator: 49
operands: 47
37Variable
38Operationoperator: 49
operands: 48
39Operationoperator: 49
operands: 50
40Lambdaparameter: 59
body: 51
41Variable
42Lambdaparameter: 59
body: 52
43Variable
44Lambdaparameter: 59
body: 53
45Literal
46Variable
47ExprTuple51, 54
48ExprTuple52, 54
49Literal
50ExprTuple53, 54
51IndexedVarvariable: 55
index: 59
52IndexedVarvariable: 56
index: 59
53IndexedVarvariable: 57
index: 59
54Literal
55Variable
56Variable
57Variable
58ExprTuple59
59Variable