logo

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, V, a, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Forall, InSet
In [2]:
# build up the expression from sub-expressions
expr = Lambda(a, Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(ScalarMult(a, x), V), domain = V), InSet(a, 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())
a \mapsto \left\{\forall_{x \in V}~\left(\left(a \cdot x\right) \in V\right) \textrm{ if } a \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
0Lambdaparameter: 21
body: 2
1ExprTuple21
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 15
operands: 7
5Literal
6ExprTuple8
7ExprTuple21, 9
8Lambdaparameter: 22
body: 11
9Variable
10ExprTuple22
11Conditionalvalue: 12
condition: 13
12Operationoperator: 15
operands: 14
13Operationoperator: 15
operands: 16
14ExprTuple17, 18
15Literal
16ExprTuple22, 18
17Operationoperator: 19
operands: 20
18Variable
19Literal
20ExprTuple21, 22
21Variable
22Variable