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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 ExprTuple, Lambda, P, Q
from proveit.logic import Implies, Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_forall__Py_not_T__st_Qy
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([P, Q], Implies(general_exists_Px_st_Qx, Not(general_forall__Py_not_T__st_Qy)).with_wrapping_at(2)))
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(P, Q\right) \mapsto \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)\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
2ExprTuple33, 28
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7
6Operationoperator: 8
operand: 12
7Operationoperator: 10
operand: 13
8Literal
9ExprTuple12
10Literal
11ExprTuple13
12Lambdaparameters: 20
body: 14
13Operationoperator: 15
operand: 19
14Conditionalvalue: 17
condition: 18
15Literal
16ExprTuple19
17Operationoperator: 33
operands: 20
18Operationoperator: 28
operands: 20
19Lambdaparameters: 34
body: 21
20ExprTuple22
21Conditionalvalue: 23
condition: 24
22ExprRangelambda_map: 25
start_index: 37
end_index: 38
23Operationoperator: 26
operands: 27
24Operationoperator: 28
operands: 34
25Lambdaparameter: 42
body: 29
26Literal
27ExprTuple30, 31
28Variable
29IndexedVarvariable: 32
index: 42
30Operationoperator: 33
operands: 34
31Literal
32Variable
33Variable
34ExprTuple35
35ExprRangelambda_map: 36
start_index: 37
end_index: 38
36Lambdaparameter: 42
body: 39
37Literal
38Variable
39IndexedVarvariable: 40
index: 42
40Variable
41ExprTuple42
42Variable