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.
# 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 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 = Or(A_1_to_l, C, B_1_to_m, D_1_to_n), condition = Or(A_1_to_l, B_1_to_m, C, D_1_to_n)), 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}~|~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}}~\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)\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
3ExprTuple31, 33, 36
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple12, 13, 14
11Lambdaparameters: 25
body: 15
12Operationoperator: 18
operands: 16
13Operationoperator: 18
operands: 17
14Operationoperator: 18
operands: 19
15Conditionalvalue: 20
condition: 21
16ExprTuple31, 22
17ExprTuple33, 22
18Literal
19ExprTuple36, 22
20Operationoperator: 24
operands: 23
21Operationoperator: 24
operands: 25
22Literal
23ExprTuple26, 28, 27, 29
24Literal
25ExprTuple26, 27, 28, 29
26ExprRangelambda_map: 30
start_index: 35
end_index: 31
27ExprRangelambda_map: 32
start_index: 35
end_index: 33
28Variable
29ExprRangelambda_map: 34
start_index: 35
end_index: 36
30Lambdaparameter: 44
body: 37
31Variable
32Lambdaparameter: 44
body: 38
33Variable
34Lambdaparameter: 44
body: 39
35Literal
36Variable
37IndexedVarvariable: 40
index: 44
38IndexedVarvariable: 41
index: 44
39IndexedVarvariable: 42
index: 44
40Variable
41Variable
42Variable
43ExprTuple44
44Variable