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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 Conditional, ExprTuple, Lambda, m, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall, InSet, NotInSet, Union
from proveit.logic.sets import x_notin_all_A
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = Equals(NotInSet(x, Union(A_1_to_m)), x_notin_all_A)), InSet(m, NaturalPos))))
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(m \mapsto \left\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}}~\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) \textrm{ if } m \in \mathbb{N}^+\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
1Lambdaparameter: 30
body: 3
2ExprTuple30
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple30, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple33, 26
13Operationoperator: 14
operands: 15
14Literal
15ExprTuple16, 17
16Operationoperator: 31
operands: 18
17Operationoperator: 19
operands: 20
18ExprTuple33, 21
19Literal
20ExprTuple22
21Operationoperator: 23
operands: 24
22ExprRangelambda_map: 25
start_index: 29
end_index: 30
23Literal
24ExprTuple26
25Lambdaparameter: 37
body: 27
26ExprRangelambda_map: 28
start_index: 29
end_index: 30
27Operationoperator: 31
operands: 32
28Lambdaparameter: 37
body: 34
29Literal
30Variable
31Literal
32ExprTuple33, 34
33Variable
34IndexedVarvariable: 35
index: 37
35Variable
36ExprTuple37
37Variable