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Expression of type Forall

from the theory of proveit.logic.sets.enumeration

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 x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Forall, InSet, Set
from proveit.logic.sets import x_equals_any_y
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = x_equals_any_y, condition = InSet(x, Set(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_{x, y_{1}, y_{2}, \ldots, y_{n}~|~x \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}}~\left(\left(x = y_{1}\right) \lor  \left(x = y_{2}\right) \lor  \ldots \lor  \left(x = y_{n}\right)\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
4ExprTuple24, 18
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12
10Literal
11ExprTuple24, 13
12ExprRangelambda_map: 14
start_index: 22
end_index: 23
13Operationoperator: 15
operands: 16
14Lambdaparameter: 28
body: 17
15Literal
16ExprTuple18
17Operationoperator: 19
operands: 20
18ExprRangelambda_map: 21
start_index: 22
end_index: 23
19Literal
20ExprTuple24, 25
21Lambdaparameter: 28
body: 25
22Literal
23Variable
24Variable
25IndexedVarvariable: 26
index: 28
26Variable
27ExprTuple28
28Variable