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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, alpha
from proveit.core_expr_types import P__x_1_to_n, Q__x_1_to_n, x_1_to_n
from proveit.logic import And, Forall, Implies
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([P, Q], Implies(And(general_exists_Py_st_Qy, Forall(instance_param_or_params = [x_1_to_n], instance_expr = Implies(P__x_1_to_n, alpha), condition = Q__x_1_to_n)), alpha)))
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(\left(\left[\exists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \land \left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow \alpha\right)\right]\right) \Rightarrow \alpha\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
2ExprTuple30, 25
3Operationoperator: 23
operands: 4
4ExprTuple5, 28
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 10
operand: 14
9Operationoperator: 12
operand: 15
10Literal
11ExprTuple14
12Literal
13ExprTuple15
14Lambdaparameters: 22
body: 16
15Lambdaparameters: 31
body: 17
16Conditionalvalue: 18
condition: 19
17Conditionalvalue: 20
condition: 21
18Operationoperator: 30
operands: 22
19Operationoperator: 25
operands: 22
20Operationoperator: 23
operands: 24
21Operationoperator: 25
operands: 31
22ExprTuple26
23Literal
24ExprTuple27, 28
25Variable
26ExprRangelambda_map: 29
start_index: 36
end_index: 37
27Operationoperator: 30
operands: 31
28Variable
29Lambdaparameter: 41
body: 32
30Variable
31ExprTuple33
32IndexedVarvariable: 34
index: 41
33ExprRangelambda_map: 35
start_index: 36
end_index: 37
34Variable
35Lambdaparameter: 41
body: 38
36Literal
37Variable
38IndexedVarvariable: 39
index: 41
39Variable
40ExprTuple41
41Variable