# from the theory of proveit.logic.sets.enumeration¶

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 n, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Forall, InSet, Set
from proveit.logic.sets import x_equals_any_y
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = x_equals_any_y, condition = InSet(x, Set(y_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_{n \in \mathbb{N}}~\left[\forall_{x, y_{1}, y_{2}, \ldots, y_{n}~|~x \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}}~\left(\left(x = y_{1}\right) \lor  \left(x = y_{2}\right) \lor  \ldots \lor  \left(x = y_{n}\right)\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
2Lambdaparameter: 31
body: 4
3ExprTuple31
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 18
operands: 9
7Literal
8ExprTuple10
9ExprTuple31, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple32, 26
13Conditionalvalue: 14
condition: 15
14Operationoperator: 16
operands: 17
15Operationoperator: 18
operands: 19
16Literal
17ExprTuple20
18Literal
19ExprTuple32, 21
20ExprRangelambda_map: 22
start_index: 30
end_index: 31
21Operationoperator: 23
operands: 24
22Lambdaparameter: 36
body: 25
23Literal
24ExprTuple26
25Operationoperator: 27
operands: 28
26ExprRangelambda_map: 29
start_index: 30
end_index: 31
27Literal
28ExprTuple32, 33
29Lambdaparameter: 36
body: 33
30Literal
31Variable
32Variable
33IndexedVarvariable: 34
index: 36
34Variable
35ExprTuple36
36Variable