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Expression of type Lambda

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, Conditional, K, Lambda, V
from proveit.linear_algebra import TensorProd, VecSpaces
from proveit.logic import Equals, Forall, InClass
In [2]:
# build up the expression from sub-expressions
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [A], instance_expr = Equals(TensorProd(A), A), domain = V), InClass(V, VecSpaces(K))))
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())
V \mapsto \left\{\forall_{A \in V}~\left(\left[{\otimes}\right]\left(A\right) = A\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 22
body: 2
1ExprTuple22
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple22, 10
9Lambdaparameter: 25
body: 11
10Operationoperator: 12
operand: 16
11Conditionalvalue: 14
condition: 15
12Literal
13ExprTuple16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Variable
17Literal
18ExprTuple21, 25
19Literal
20ExprTuple25, 22
21Operationoperator: 23
operand: 25
22Variable
23Literal
24ExprTuple25
25Variable