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Expression of type Lambda

from the theory of proveit.linear_algebra.scalar_multiplication

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, K, Lambda, alpha, beta, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import And, Equals, InSet
In [2]:
# build up the expression from sub-expressions
expr = Lambda([alpha, beta], Conditional(Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), And(InSet(alpha, K), InSet(beta, 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())
\left(\alpha, \beta\right) \mapsto \left\{\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right) \textrm{ if } \alpha \in K ,  \beta \in K\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 22
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple10, 11
8Operationoperator: 21
operands: 12
9Operationoperator: 21
operands: 13
10Operationoperator: 15
operands: 14
11Operationoperator: 15
operands: 16
12ExprTuple24, 17
13ExprTuple18, 23
14ExprTuple24, 19
15Literal
16ExprTuple25, 19
17Operationoperator: 21
operands: 20
18Operationoperator: 21
operands: 22
19Variable
20ExprTuple25, 23
21Literal
22ExprTuple24, 25
23Variable
24Variable
25Variable