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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, 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 = 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\{\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..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 21
operand: 6
2Operationoperator: 4
operands: 5
3ExprTuple6
4Literal
5ExprTuple44, 7
6Lambdaparameters: 8
body: 9
7Literal
8ExprTuple39, 34
9Operationoperator: 10
operands: 11
10Literal
11ExprTuple12, 13
12Operationoperator: 14
operand: 18
13Operationoperator: 16
operand: 19
14Literal
15ExprTuple18
16Literal
17ExprTuple19
18Lambdaparameters: 26
body: 20
19Operationoperator: 21
operand: 25
20Conditionalvalue: 23
condition: 24
21Literal
22ExprTuple25
23Operationoperator: 39
operands: 26
24Operationoperator: 34
operands: 26
25Lambdaparameters: 40
body: 27
26ExprTuple28
27Conditionalvalue: 29
condition: 30
28ExprRangelambda_map: 31
start_index: 43
end_index: 44
29Operationoperator: 32
operands: 33
30Operationoperator: 34
operands: 40
31Lambdaparameter: 48
body: 35
32Literal
33ExprTuple36, 37
34Variable
35IndexedVarvariable: 38
index: 48
36Operationoperator: 39
operands: 40
37Literal
38Variable
39Variable
40ExprTuple41
41ExprRangelambda_map: 42
start_index: 43
end_index: 44
42Lambdaparameter: 48
body: 45
43Literal
44Variable
45IndexedVarvariable: 46
index: 48
46Variable
47ExprTuple48
48Variable