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, C, D
from proveit.logic import Boolean, Forall, Implies, Not, Or
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B, C, D], instance_expr = Or(Not(A), Not(B)), domain = Boolean, conditions = [Or(Not(C), Not(D)), Implies(A, C), Implies(B, D)])
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, C, D \in \mathbb{B}~|~(\lnot C) \lor (\lnot D), A \Rightarrow C, B \Rightarrow D}~\left((\lnot A) \lor (\lnot B)\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
4ExprTuple35, 36, 40, 41
5Conditionalvalue: 6
condition: 7
6Operationoperator: 27
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple13, 14, 15, 16, 17, 18, 19
11Operationoperator: 38
operand: 35
12Operationoperator: 38
operand: 36
13Operationoperator: 25
operands: 22
14Operationoperator: 25
operands: 23
15Operationoperator: 25
operands: 24
16Operationoperator: 25
operands: 26
17Operationoperator: 27
operands: 28
18Operationoperator: 30
operands: 29
19Operationoperator: 30
operands: 31
20ExprTuple35
21ExprTuple36
22ExprTuple35, 32
23ExprTuple36, 32
24ExprTuple40, 32
25Literal
26ExprTuple41, 32
27Literal
28ExprTuple33, 34
29ExprTuple35, 40
30Literal
31ExprTuple36, 41
32Literal
33Operationoperator: 38
operand: 40
34Operationoperator: 38
operand: 41
35Variable
36Variable
37ExprTuple40
38Literal
39ExprTuple41
40Variable
41Variable