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Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification.existence

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, P, n
from proveit.core_expr_types import P__y_1_to_n, y_1_to_n
from proveit.logic import Forall, InSet
from proveit.logic.booleans.quantification import general_exists_Px
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [y_1_to_n], instance_expr = general_exists_Px, condition = P__y_1_to_n)), InSet(n, 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(n \mapsto \left\{\forall_{P}~\left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left[\exists_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right]\right] \textrm{ if } n \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: 33
body: 3
2ExprTuple33
3Conditionalvalue: 4
condition: 5
4Operationoperator: 13
operand: 9
5Operationoperator: 7
operands: 8
6ExprTuple9
7Literal
8ExprTuple33, 10
9Lambdaparameter: 26
body: 12
10Literal
11ExprTuple26
12Operationoperator: 13
operand: 15
13Literal
14ExprTuple15
15Lambdaparameters: 21
body: 16
16Conditionalvalue: 17
condition: 18
17Operationoperator: 19
operand: 22
18Operationoperator: 26
operands: 21
19Literal
20ExprTuple22
21ExprTuple23
22Lambdaparameters: 27
body: 24
23ExprRangelambda_map: 25
start_index: 32
end_index: 33
24Operationoperator: 26
operands: 27
25Lambdaparameter: 37
body: 28
26Variable
27ExprTuple29
28IndexedVarvariable: 30
index: 37
29ExprRangelambda_map: 31
start_index: 32
end_index: 33
30Variable
31Lambdaparameter: 37
body: 34
32Literal
33Variable
34IndexedVarvariable: 35
index: 37
35Variable
36ExprTuple37
37Variable