logo

Expression of type Forall

from the theory of proveit.logic.sets.unification

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 A_1_to_m
from proveit.logic import Equals, Forall, NotInSet, Union
from proveit.logic.sets import x_notin_all_A
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = Equals(NotInSet(x, Union(A_1_to_m)), x_notin_all_A))
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, A_{1}, A_{2}, \ldots, A_{m}}~\left(\left(x \notin \left(A_{1} \cup  A_{2} \cup  \ldots \cup  A_{m}\right)\right) = \left(\left(x \notin A_{1}\right) \land  \left(x \notin A_{2}\right) \land  \ldots \land  \left(x \notin A_{m}\right)\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
4ExprTuple25, 18
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 23
operands: 10
9Operationoperator: 11
operands: 12
10ExprTuple25, 13
11Literal
12ExprTuple14
13Operationoperator: 15
operands: 16
14ExprRangelambda_map: 17
start_index: 21
end_index: 22
15Literal
16ExprTuple18
17Lambdaparameter: 29
body: 19
18ExprRangelambda_map: 20
start_index: 21
end_index: 22
19Operationoperator: 23
operands: 24
20Lambdaparameter: 29
body: 26
21Literal
22Variable
23Literal
24ExprTuple25, 26
25Variable
26IndexedVarvariable: 27
index: 29
27Variable
28ExprTuple29
29Variable