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Expression of type Forall

from the theory of proveit.logic.sets.functions

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, f, fx, x
from proveit.logic import Equals, Forall, Functions, InSet
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, A, B], instance_expr = Equals(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [x], instance_expr = InSet(fx, B), domain = A)))
Out[2]:
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_{f, A, B}~\left(\left(f \in \left[A \rightarrow B\right])\right) = \left[\forall_{x \in A}~\left(f\left(x\right) \in B\right)\right]\right)
In [5]:
stored_expr.style_options()
Out[5]:
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()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 10
operand: 2
1ExprTuple2
2Lambdaparameters: 3
body: 4
3ExprTuple25, 24, 23
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 20
operands: 9
8Operationoperator: 10
operand: 13
9ExprTuple25, 12
10Literal
11ExprTuple13
12Operationoperator: 14
operands: 15
13Lambdaparameter: 27
body: 16
14Literal
15ExprTuple24, 23
16Conditionalvalue: 17
condition: 18
17Operationoperator: 20
operands: 19
18Operationoperator: 20
operands: 21
19ExprTuple22, 23
20Literal
21ExprTuple27, 24
22Operationoperator: 25
operand: 27
23Variable
24Variable
25Variable
26ExprTuple27
27Variable