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Expression of type Forall

from the theory of proveit.logic.booleans.quantification

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.core_expr_types import P__x_1_to_m_y_1_to_n, R__x_1_to_m_y_1_to_n, y_1_to_n
from proveit.logic import Forall
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [y_1_to_n], instance_expr = P__x_1_to_m_y_1_to_n, condition = R__x_1_to_m_y_1_to_n)
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())
\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple12
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 10
7Operationoperator: 9
operands: 10
8Variable
9Variable
10ExprTuple11, 12
11ExprRangelambda_map: 13
start_index: 16
end_index: 14
12ExprRangelambda_map: 15
start_index: 16
end_index: 17
13Lambdaparameter: 23
body: 18
14Variable
15Lambdaparameter: 23
body: 19
16Literal
17Variable
18IndexedVarvariable: 20
index: 23
19IndexedVarvariable: 21
index: 23
20Variable
21Variable
22ExprTuple23
23Variable