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Expression of type Lambda

from the theory of proveit.linear_algebra

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 Conditional, Lambda, S, V, W
from proveit.linear_algebra import LinMap, LinMapAdd
from proveit.logic import Equals, InSet
In [2]:
# build up the expression from sub-expressions
expr = Lambda(S, Conditional(Equals(LinMapAdd(S), S), InSet(S, LinMap(V, W))))
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())
S \mapsto \left\{\left[+\right]\left(S\right) = S \textrm{ if } S \in \mathcal{L}\left(V, W\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: 14
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 14
6Literal
7ExprTuple14, 9
8Operationoperator: 10
operand: 14
9Operationoperator: 12
operands: 13
10Literal
11ExprTuple14
12Literal
13ExprTuple15, 16
14Variable
15Variable
16Variable