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Expression of type Forall

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, 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 Boolean, Equals, Forall, Or
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l, m, n], instance_expr = 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), domain = 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())
\forall_{l, m, n \in \mathbb{N}}~\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)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple46, 48, 51
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 23
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12, 13
10Lambdaparameters: 31
body: 14
11Operationoperator: 54
operands: 15
12Operationoperator: 54
operands: 16
13Operationoperator: 54
operands: 17
14Conditionalvalue: 18
condition: 19
15ExprTuple46, 20
16ExprTuple48, 20
17ExprTuple51, 20
18Operationoperator: 21
operands: 22
19Operationoperator: 23
operands: 24
20Literal
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple27, 28, 29, 30
25Operationoperator: 32
operands: 31
26Operationoperator: 32
operands: 33
27ExprRangelambda_map: 34
start_index: 50
end_index: 46
28ExprRangelambda_map: 35
start_index: 50
end_index: 48
29Operationoperator: 54
operands: 36
30ExprRangelambda_map: 37
start_index: 50
end_index: 51
31ExprTuple38, 39, 43, 40
32Literal
33ExprTuple38, 43, 39, 40
34Lambdaparameter: 64
body: 41
35Lambdaparameter: 64
body: 42
36ExprTuple43, 59
37Lambdaparameter: 64
body: 44
38ExprRangelambda_map: 45
start_index: 50
end_index: 46
39ExprRangelambda_map: 47
start_index: 50
end_index: 48
40ExprRangelambda_map: 49
start_index: 50
end_index: 51
41Operationoperator: 54
operands: 52
42Operationoperator: 54
operands: 53
43Variable
44Operationoperator: 54
operands: 55
45Lambdaparameter: 64
body: 56
46Variable
47Lambdaparameter: 64
body: 57
48Variable
49Lambdaparameter: 64
body: 58
50Literal
51Variable
52ExprTuple56, 59
53ExprTuple57, 59
54Literal
55ExprTuple58, 59
56IndexedVarvariable: 60
index: 64
57IndexedVarvariable: 61
index: 64
58IndexedVarvariable: 62
index: 64
59Literal
60Variable
61Variable
62Variable
63ExprTuple64
64Variable