# 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 equal_element_equality
In [2]:
# check that the built expression is the same as the stored expression
assert equal_element_equality.expr == stored_expr
assert equal_element_equality.expr._style_id == stored_expr._style_id
print("Passed sanity check: equal_element_equality matches stored_expr")
Passed sanity check: equal_element_equality matches stored_expr
In [3]:
# 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}, d~|~b = d}~\left(\begin{array}{c} \begin{array}{l} \left\{a_{1}, a_{2}, \ldots, a_{m}, b,c_{1}, c_{2}, \ldots, c_{n}\right\} =  \\ \left\{a_{1}, a_{2}, \ldots, a_{m}, d,c_{1}, c_{2}, \ldots, c_{n}\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
3ExprTuple35, 38
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple12, 13
11Lambdaparameters: 14
body: 15
12Operationoperator: 17
operands: 16
13Operationoperator: 17
operands: 18
14ExprTuple31, 30, 33, 32
15Conditionalvalue: 19
condition: 20
16ExprTuple35, 21
17Literal
18ExprTuple38, 21
19Operationoperator: 23
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple25, 26
23Literal
24ExprTuple30, 32
25Operationoperator: 28
operands: 27
26Operationoperator: 28
operands: 29
27ExprTuple31, 30, 33
28Literal
29ExprTuple31, 32, 33
30Variable
31ExprRangelambda_map: 34
start_index: 37
end_index: 35
32Variable
33ExprRangelambda_map: 36
start_index: 37
end_index: 38
34Lambdaparameter: 44
body: 39
35Variable
36Lambdaparameter: 44
body: 40
37Literal
38Variable
39IndexedVarvariable: 41
index: 44
40IndexedVarvariable: 42
index: 44
41Variable
42Variable
43ExprTuple44
44Variable