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Expression of type Forall

from the theory of proveit.logic.booleans.conjunction

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
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Boolean, Forall, InSet
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(And(A_1_to_m), Boolean), domain = Boolean), 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 \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m} \in \mathbb{B}}~\left(\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m}\right) \in \mathbb{B}\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
2Lambdaparameter: 26
body: 4
3ExprTuple26
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 27
operands: 9
7Literal
8ExprTuple10
9ExprTuple26, 11
10Lambdaparameters: 20
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 27
operands: 15
14Operationoperator: 19
operands: 16
15ExprTuple17, 30
16ExprTuple18
17Operationoperator: 19
operands: 20
18ExprRangelambda_map: 21
start_index: 25
end_index: 26
19Literal
20ExprTuple22
21Lambdaparameter: 33
body: 23
22ExprRangelambda_map: 24
start_index: 25
end_index: 26
23Operationoperator: 27
operands: 28
24Lambdaparameter: 33
body: 29
25Literal
26Variable
27Literal
28ExprTuple29, 30
29IndexedVarvariable: 31
index: 33
30Literal
31Variable
32ExprTuple33
33Variable