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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, Q, n
from proveit.logic import Forall, Implies, InSet, Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_forall__Py_not_T__st_Qy
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, Q], instance_expr = Implies(general_exists_Px_st_Qx, Not(general_forall__Py_not_T__st_Qy)).with_wrapping_at(2)), 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, Q}~\left(\begin{array}{c} \begin{array}{l} \left[\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ (\lnot \left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \neq \top\right)\right]) \end{array} \end{array}\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: 47
body: 3
2ExprTuple47
3Conditionalvalue: 4
condition: 5
4Operationoperator: 24
operand: 9
5Operationoperator: 7
operands: 8
6ExprTuple9
7Literal
8ExprTuple47, 10
9Lambdaparameters: 11
body: 12
10Literal
11ExprTuple42, 37
12Operationoperator: 13
operands: 14
13Literal
14ExprTuple15, 16
15Operationoperator: 17
operand: 21
16Operationoperator: 19
operand: 22
17Literal
18ExprTuple21
19Literal
20ExprTuple22
21Lambdaparameters: 29
body: 23
22Operationoperator: 24
operand: 28
23Conditionalvalue: 26
condition: 27
24Literal
25ExprTuple28
26Operationoperator: 42
operands: 29
27Operationoperator: 37
operands: 29
28Lambdaparameters: 43
body: 30
29ExprTuple31
30Conditionalvalue: 32
condition: 33
31ExprRangelambda_map: 34
start_index: 46
end_index: 47
32Operationoperator: 35
operands: 36
33Operationoperator: 37
operands: 43
34Lambdaparameter: 51
body: 38
35Literal
36ExprTuple39, 40
37Variable
38IndexedVarvariable: 41
index: 51
39Operationoperator: 42
operands: 43
40Literal
41Variable
42Variable
43ExprTuple44
44ExprRangelambda_map: 45
start_index: 46
end_index: 47
45Lambdaparameter: 51
body: 48
46Literal
47Variable
48IndexedVarvariable: 49
index: 51
49Variable
50ExprTuple51
51Variable