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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, Union
from proveit.logic.sets import x_in_any_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(InSet(x, Union(A_1_to_m)), x_in_any_A).with_wrapping_at(2)), 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(\begin{array}{c} \begin{array}{l} \left(x \in \left(A_{1} \cup  A_{2} \cup  \ldots \cup  A_{m}\right)\right) =  \\ \left(\left(x \in A_{1}\right) \lor  \left(x \in A_{2}\right) \lor  \ldots \lor  \left(x \in A_{m}\right)\right) \end{array} \end{array}\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: 29
body: 3
2ExprTuple29
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 30
operands: 8
6Literal
7ExprTuple9
8ExprTuple29, 10
9Lambdaparameters: 11
body: 12
10Literal
11ExprTuple32, 25
12Operationoperator: 13
operands: 14
13Literal
14ExprTuple15, 16
15Operationoperator: 30
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple32, 20
18Literal
19ExprTuple21
20Operationoperator: 22
operands: 23
21ExprRangelambda_map: 24
start_index: 28
end_index: 29
22Literal
23ExprTuple25
24Lambdaparameter: 36
body: 26
25ExprRangelambda_map: 27
start_index: 28
end_index: 29
26Operationoperator: 30
operands: 31
27Lambdaparameter: 36
body: 33
28Literal
29Variable
30Literal
31ExprTuple32, 33
32Variable
33IndexedVarvariable: 34
index: 36
34Variable
35ExprTuple36
36Variable