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Expression of type Lambda

from the theory of proveit.linear_algebra.addition

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, Function, Lambda, k, t, v
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Neg, one, subtract, two, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Function(v, [subtract(k, Neg(one))]), InSet(k, Interval(subtract(zero, one), subtract(Exp(two, t), one)))))
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())
k \mapsto \left\{v\left(k - \left(-1\right)\right) \textrm{ if } k \in \{0 - 1~\ldotp \ldotp~2^{t} - 1\}\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: 2
1ExprTuple14
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Variable
6ExprTuple9
7Literal
8ExprTuple14, 10
9Operationoperator: 20
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 15
12Literal
13ExprTuple16, 17
14Variable
15Operationoperator: 27
operand: 24
16Operationoperator: 20
operands: 19
17Operationoperator: 20
operands: 21
18ExprTuple24
19ExprTuple22, 24
20Literal
21ExprTuple23, 24
22Literal
23Operationoperator: 25
operands: 26
24Operationoperator: 27
operand: 31
25Literal
26ExprTuple29, 30
27Literal
28ExprTuple31
29Literal
30Variable
31Literal