logo

Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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 A, B
from proveit.logic import Boolean, Forall, Not, Or
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B], instance_expr = B, domain = Boolean, conditions = [Or(A, B), Not(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_{A, B \in \mathbb{B}~|~A \lor B, \lnot A}~B
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: 16
body: 4
4Conditionalvalue: 20
condition: 5
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9, 10, 11
8Operationoperator: 13
operands: 12
9Operationoperator: 13
operands: 14
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operand: 21
12ExprTuple21, 19
13Literal
14ExprTuple20, 19
15Literal
16ExprTuple21, 20
17Literal
18ExprTuple21
19Literal
20Variable
21Variable