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Expression of type Implies

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.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 = 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())
\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}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()(2)('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operand: 10
5Literal
6ExprTuple9
7Literal
8ExprTuple10
9Lambdaparameters: 17
body: 11
10Operationoperator: 12
operand: 16
11Conditionalvalue: 14
condition: 15
12Literal
13ExprTuple16
14Operationoperator: 30
operands: 17
15Operationoperator: 25
operands: 17
16Lambdaparameters: 31
body: 18
17ExprTuple19
18Conditionalvalue: 20
condition: 21
19ExprRangelambda_map: 22
start_index: 34
end_index: 35
20Operationoperator: 23
operands: 24
21Operationoperator: 25
operands: 31
22Lambdaparameter: 39
body: 26
23Literal
24ExprTuple27, 28
25Variable
26IndexedVarvariable: 29
index: 39
27Operationoperator: 30
operands: 31
28Literal
29Variable
30Variable
31ExprTuple32
32ExprRangelambda_map: 33
start_index: 34
end_index: 35
33Lambdaparameter: 39
body: 36
34Literal
35Variable
36IndexedVarvariable: 37
index: 39
37Variable
38ExprTuple39
39Variable