logo

Expression of type Forall

from the theory of proveit.linear_algebra.tensors

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 fi, i, x, y
from proveit.linear_algebra import TensorProd
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Interval, Real, four, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
expr = Forall(instance_param_or_params = [i], instance_expr = InSet(TensorProd(x, fi, y), TensorProd(sub_expr1, sub_expr1, sub_expr1)), domain = Interval(two, four))
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_{i \in \{2~\ldotp \ldotp~4\}}~\left(\left(x {\otimes} f\left(i\right) {\otimes} y\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\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
3Lambdaparameter: 28
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple28, 12
10Operationoperator: 14
operands: 13
11Operationoperator: 14
operands: 15
12Operationoperator: 16
operands: 17
13ExprTuple18, 19, 20
14Literal
15ExprTuple21, 21, 21
16Literal
17ExprTuple22, 23
18Variable
19Operationoperator: 24
operand: 28
20Variable
21Operationoperator: 26
operands: 27
22Literal
23Literal
24Variable
25ExprTuple28
26Literal
27ExprTuple29, 30
28Variable
29Literal
30Literal