# 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 B, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import Boolean, Forall, Or
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m, n], instance_expr = Forall(instance_param_or_params = [A_1_to_m, B, C_1_to_n], instance_expr = Or(A_1_to_m, B, C_1_to_n), domain = Boolean, condition = B), 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_{m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m}, B, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}~|~B}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{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, 35
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 21
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12
10Lambdaparameters: 20
body: 13
11Operationoperator: 40
operands: 14
12Operationoperator: 40
operands: 15
13Conditionalvalue: 16
condition: 17
14ExprTuple31, 18
15ExprTuple35, 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18Literal
19Literal
20ExprTuple23, 37, 24
21Literal
22ExprTuple25, 26, 27, 37
23ExprRangelambda_map: 28
start_index: 34
end_index: 31
24ExprRangelambda_map: 29
start_index: 34
end_index: 35
25ExprRangelambda_map: 30
start_index: 34
end_index: 31
26Operationoperator: 40
operands: 32
27ExprRangelambda_map: 33
start_index: 34
end_index: 35
28Lambdaparameter: 48
body: 42
29Lambdaparameter: 48
body: 43
30Lambdaparameter: 48
body: 36
31Variable
32ExprTuple37, 44
33Lambdaparameter: 48
body: 38
34Literal
35Variable
36Operationoperator: 40
operands: 39
37Variable
38Operationoperator: 40
operands: 41
39ExprTuple42, 44
40Literal
41ExprTuple43, 44
42IndexedVarvariable: 45
index: 48
43IndexedVarvariable: 46
index: 48
44Literal
45Variable
46Variable
47ExprTuple48
48Variable