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Expression of type ExprTuple

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, Lambda, b
from proveit.core_expr_types import a_1_to_i, c_1_to_j, d_1_to_k
from proveit.logic import Equals, Set
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a_1_to_i, b, c_1_to_j, d_1_to_k], Equals(Set(a_1_to_i, b, c_1_to_j, d_1_to_k), Set(a_1_to_i, c_1_to_j, b, d_1_to_k))))
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())
\left(\left(a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j}, d_{1}, d_{2}, \ldots, d_{k}\right) \mapsto \left(\left\{a_{1}, a_{2}, \ldots, a_{i}, b,c_{1}, c_{2}, \ldots, c_{j},d_{1}, d_{2}, \ldots, d_{k}\right\} = \left\{a_{1}, a_{2}, \ldots, a_{i},c_{1}, c_{2}, \ldots, c_{j}, b,d_{1}, d_{2}, \ldots, d_{k}\right\}\right)\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 7
body: 2
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 12, 11, 13
8Literal
9ExprTuple10, 11, 12, 13
10ExprRangelambda_map: 14
start_index: 19
end_index: 15
11ExprRangelambda_map: 16
start_index: 19
end_index: 17
12Variable
13ExprRangelambda_map: 18
start_index: 19
end_index: 20
14Lambdaparameter: 28
body: 21
15Variable
16Lambdaparameter: 28
body: 22
17Variable
18Lambdaparameter: 28
body: 23
19Literal
20Variable
21IndexedVarvariable: 24
index: 28
22IndexedVarvariable: 25
index: 28
23IndexedVarvariable: 26
index: 28
24Variable
25Variable
26Variable
27ExprTuple28
28Variable