logo

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 m, n
from proveit.core_expr_types import a_1_to_m, b_1_to_n
from proveit.logic import Forall, Set, SubsetEq
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m, n], instance_expr = Forall(instance_param_or_params = [a_1_to_m, b_1_to_n], instance_expr = SubsetEq(Set(a_1_to_m), Set(a_1_to_m, b_1_to_n))), domain = Natural)
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_{m, n \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{n}}~\left(\left\{a_{1}, a_{2}, \ldots, a_{m}\right\} \subseteq \left\{a_{1}, a_{2}, \ldots, a_{m},b_{1}, b_{2}, \ldots, b_{n}\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: 7
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple29, 32
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple12, 13
11Lambdaparameters: 25
body: 14
12Operationoperator: 16
operands: 15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operands: 19
15ExprTuple29, 20
16Literal
17ExprTuple32, 20
18Literal
19ExprTuple21, 22
20Literal
21Operationoperator: 24
operands: 23
22Operationoperator: 24
operands: 25
23ExprTuple26
24Literal
25ExprTuple26, 27
26ExprRangelambda_map: 28
start_index: 31
end_index: 29
27ExprRangelambda_map: 30
start_index: 31
end_index: 32
28Lambdaparameter: 38
body: 33
29Variable
30Lambdaparameter: 38
body: 34
31Literal
32Variable
33IndexedVarvariable: 35
index: 38
34IndexedVarvariable: 36
index: 38
35Variable
36Variable
37ExprTuple38
38Variable