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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
from proveit.logic import Boolean, Forall, Implies, Or
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B], instance_expr = Forall(instance_param_or_params = [C], instance_expr = C, conditions = [Implies(A, C), Implies(B, C)]), domain = Boolean, condition = Or(A, B))
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}~\left[\forall_{C~|~A \Rightarrow C, B \Rightarrow C}~C\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: 6
operand: 2
1ExprTuple2
2Lambdaparameters: 19
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 9
5Operationoperator: 22
operands: 8
6Literal
7ExprTuple9
8ExprTuple10, 11, 12
9Lambdaparameter: 31
body: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12Operationoperator: 18
operands: 19
13ExprTuple31
14Conditionalvalue: 31
condition: 20
15ExprTuple29, 21
16Literal
17ExprTuple30, 21
18Literal
19ExprTuple29, 30
20Operationoperator: 22
operands: 23
21Literal
22Literal
23ExprTuple24, 25
24Operationoperator: 27
operands: 26
25Operationoperator: 27
operands: 28
26ExprTuple29, 31
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Variable