logo

Expression of type Lambda

from the theory of proveit.numbers.division

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, x, y, z
from proveit.logic import Equals, InSet
from proveit.numbers import Complex, Mult, frac
In [2]:
# build up the expression from sub-expressions
expr = Lambda(y, Conditional(Equals(frac(Mult(y, x), Mult(z, x)), frac(y, z)), InSet(y, Complex)))
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())
y \mapsto \left\{\frac{y \cdot x}{z \cdot x} = \frac{y}{z} \textrm{ if } y \in \mathbb{C}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 20
body: 2
1ExprTuple20
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple20, 11
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple20, 21
15Operationoperator: 18
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 22
18Literal
19ExprTuple21, 22
20Variable
21Variable
22Variable