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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 Exists, Forall, Implies, SubsetEq
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A, B, P], instance_expr = Implies(Exists(instance_param_or_params = [x], instance_expr = Px, domain = A), Exists(instance_param_or_params = [y], instance_expr = Py, domain = B)), condition = SubsetEq(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 \subseteq B}~\left(\left[\exists_{x \in A}~P\left(x\right)\right] \Rightarrow \left[\exists_{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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple32, 34, 27
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple32, 34
12Operationoperator: 15
operand: 17
13Operationoperator: 15
operand: 18
14ExprTuple17
15Literal
16ExprTuple18
17Lambdaparameter: 31
body: 19
18Lambdaparameter: 33
body: 20
19Conditionalvalue: 21
condition: 22
20Conditionalvalue: 23
condition: 24
21Operationoperator: 27
operand: 31
22Operationoperator: 29
operands: 26
23Operationoperator: 27
operand: 33
24Operationoperator: 29
operands: 30
25ExprTuple31
26ExprTuple31, 32
27Variable
28ExprTuple33
29Literal
30ExprTuple33, 34
31Variable
32Variable
33Variable
34Variable