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

see dependencies

In [1]:
import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import the special expression
from proveit.logic.sets.enumeration import reduction_right

In [2]:
# check that the built expression is the same as the stored expression
assert reduction_right.expr == stored_expr
assert reduction_right.expr._style_id == stored_expr._style_id
print("Passed sanity check: reduction_right matches stored_expr")

Passed sanity check: reduction_right matches stored_expr

In [3]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{i, j, k \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, x, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}}~\left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{i}, x,b_{1}, b_{2}, \ldots, b_{j}, x,c_{1}, c_{2}, \ldots, c_{k}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{i}, x,b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right\} \end{array} \end{array}\right)\right]

In [4]:
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 [5]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple33, 35, 38
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple12, 13, 14
11Lambdaparameters: 27
body: 15
12Operationoperator: 18
operands: 16
13Operationoperator: 18
operands: 17
14Operationoperator: 18
operands: 19
15Operationoperator: 20
operands: 21
16ExprTuple33, 22
17ExprTuple35, 22
18Literal
19ExprTuple38, 22
20Literal
21ExprTuple23, 24
22Literal
23Operationoperator: 26
operands: 25
24Operationoperator: 26
operands: 27
25ExprTuple28, 29, 30, 29, 31
26Literal
27ExprTuple28, 29, 30, 31
28ExprRangelambda_map: 32
start_index: 37
end_index: 33
29Variable
30ExprRangelambda_map: 34
start_index: 37
end_index: 35
31ExprRangelambda_map: 36
start_index: 37
end_index: 38
32Lambdaparameter: 46
body: 39
33Variable
34Lambdaparameter: 46
body: 40
35Variable
36Lambdaparameter: 46
body: 41
37Literal
38Variable
39IndexedVarvariable: 42
index: 46
40IndexedVarvariable: 43
index: 46
41IndexedVarvariable: 44
index: 46
42Variable
43Variable
44Variable
45ExprTuple46
46Variable