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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 A, K, V
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import Equals, Forall
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [K], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [A], instance_expr = Equals(TensorProd(A), A), domain = V), domain = VecSpaces(K)))
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_{K}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{A \in V}~\left(\left[{\otimes}\right]\left(A\right) = A\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
2Lambdaparameter: 21
body: 3
3Operationoperator: 10
operand: 5
4ExprTuple5
5Lambdaparameter: 27
body: 7
6ExprTuple27
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operand: 14
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14
12Literal
13ExprTuple27, 15
14Lambdaparameter: 30
body: 16
15Operationoperator: 17
operand: 21
16Conditionalvalue: 19
condition: 20
17Literal
18ExprTuple21
19Operationoperator: 22
operands: 23
20Operationoperator: 24
operands: 25
21Variable
22Literal
23ExprTuple26, 30
24Literal
25ExprTuple30, 27
26Operationoperator: 28
operand: 30
27Variable
28Literal
29ExprTuple30
30Variable