# 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 m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import Boolean, Equals, Forall, Or, TRUE
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, C_1_to_n], instance_expr = Equals(Or(A_1_to_m, TRUE, C_1_to_n), TRUE), 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_{m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor \top\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) = \top\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
3ExprTuple37, 40
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 22
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12
10Lambdaparameters: 13
body: 14
11Operationoperator: 42
operands: 15
12Operationoperator: 42
operands: 16
13ExprTuple31, 33
14Conditionalvalue: 17
condition: 18
15ExprTuple37, 19
16ExprTuple40, 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple24, 32
22Literal
23ExprTuple25, 26
24Operationoperator: 27
operands: 28
25ExprRangelambda_map: 29
start_index: 39
end_index: 37
26ExprRangelambda_map: 30
start_index: 39
end_index: 40
27Literal
28ExprTuple31, 32, 33
29Lambdaparameter: 50
body: 34
30Lambdaparameter: 50
body: 35
31ExprRangelambda_map: 36
start_index: 39
end_index: 37
32Literal
33ExprRangelambda_map: 38
start_index: 39
end_index: 40
34Operationoperator: 42
operands: 41
35Operationoperator: 42
operands: 43
36Lambdaparameter: 50
body: 44
37Variable
38Lambdaparameter: 50
body: 45
39Literal
40Variable
41ExprTuple44, 46
42Literal
43ExprTuple45, 46
44IndexedVarvariable: 47
index: 50
45IndexedVarvariable: 48
index: 50
46Literal
47Variable
48Variable
49ExprTuple50
50Variable