logo

Expression of type ExprTuple

from the theory of proveit.logic.sets.unification

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, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, NotInSet, Union
from proveit.logic.sets import x_notin_all_A
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, A_1_to_m], Equals(NotInSet(x, Union(A_1_to_m)), x_notin_all_A)))
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(x, A_{1}, A_{2}, \ldots, A_{m}\right) \mapsto \left(\left(x \notin \left(A_{1} \cup  A_{2} \cup  \ldots \cup  A_{m}\right)\right) = \left(\left(x \notin A_{1}\right) \land  \left(x \notin A_{2}\right) \land  \ldots \land  \left(x \notin A_{m}\right)\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: 2
body: 3
2ExprTuple23, 16
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7
6Operationoperator: 21
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple23, 11
9Literal
10ExprTuple12
11Operationoperator: 13
operands: 14
12ExprRangelambda_map: 15
start_index: 19
end_index: 20
13Literal
14ExprTuple16
15Lambdaparameter: 27
body: 17
16ExprRangelambda_map: 18
start_index: 19
end_index: 20
17Operationoperator: 21
operands: 22
18Lambdaparameter: 27
body: 24
19Literal
20Variable
21Literal
22ExprTuple23, 24
23Variable
24IndexedVarvariable: 25
index: 27
25Variable
26ExprTuple27
27Variable