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Expression of type Forall

from the theory of proveit.logic.sets.inclusion

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, P, Px, Py, x, y
from proveit.logic import Forall, Implies, superset_eq
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B, P], instance_expr = Implies(Forall(instance_param_or_params = [x], instance_expr = Px, domain = A), Forall(instance_param_or_params = [y], instance_expr = Py, domain = B)), condition = superset_eq(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, P~|~A \supseteq B}~\left(\left[\forall_{x \in A}~P\left(x\right)\right] \Rightarrow \left[\forall_{y \in B}~P\left(y\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: 14
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple31, 33, 26
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple33, 31
11Operationoperator: 14
operand: 16
12Operationoperator: 14
operand: 17
13ExprTuple16
14Literal
15ExprTuple17
16Lambdaparameter: 30
body: 18
17Lambdaparameter: 32
body: 19
18Conditionalvalue: 20
condition: 21
19Conditionalvalue: 22
condition: 23
20Operationoperator: 26
operand: 30
21Operationoperator: 28
operands: 25
22Operationoperator: 26
operand: 32
23Operationoperator: 28
operands: 29
24ExprTuple30
25ExprTuple30, 31
26Variable
27ExprTuple32
28Literal
29ExprTuple32, 33
30Variable
31Variable
32Variable
33Variable