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Expression of type Lambda

from the theory of proveit.numbers.absolute_value

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
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Complex
In [2]:
# build up the expression from sub-expressions
expr = Lambda([x, y], Conditional(Equals(Abs(x), Abs(y)), And(InSet(x, Complex), InSet(y, Complex), Equals(x, y))))
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(x, y\right) \mapsto \left\{\left|x\right| = \left|y\right| \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C} ,  x = y\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 19
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 18
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 8
5Literal
6ExprTuple9, 10, 11
7Operationoperator: 13
operand: 21
8Operationoperator: 13
operand: 22
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Operationoperator: 18
operands: 19
12ExprTuple21
13Literal
14ExprTuple22
15ExprTuple21, 20
16Literal
17ExprTuple22, 20
18Literal
19ExprTuple21, 22
20Literal
21Variable
22Variable