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Expression of type Forall

from the theory of proveit.logic.sets.cartesian_products

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 ExprRange, S, Variable, m
from proveit.logic import CartExp, CartProd, Equals, Forall
from proveit.numbers import NaturalPos, one
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [S], instance_expr = Equals(CartExp(S, m), CartProd(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), S, one, m)))), domain = NaturalPos)
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_{m \in \mathbb{N}^+}~\left[\forall_{S}~\left(S^{m} = \left(S \times  S \times  ..\left(m - 3\right) \times.. \times  S\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: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 26
body: 4
3ExprTuple26
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple26, 12
11Lambdaparameter: 28
body: 14
12Literal
13ExprTuple28
14Operationoperator: 15
operands: 16
15Literal
16ExprTuple17, 18
17Operationoperator: 19
operands: 20
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple28, 26
21Literal
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 29
body: 28
25Literal
26Variable
27ExprTuple29
28Variable
29Variable