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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, a, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Complex, subtract
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Abs(subtract(a, b)), Abs(subtract(b, a))), And(InSet(a, Complex), InSet(b, 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())
\left(a, b\right) \mapsto \left\{\left|a - b\right| = \left|b - a\right| \textrm{ if } a \in \mathbb{C} ,  b \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
0Lambdaparameters: 1
body: 2
1ExprTuple31, 30
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12
9Operationoperator: 14
operand: 19
10Operationoperator: 14
operand: 20
11Operationoperator: 17
operands: 16
12Operationoperator: 17
operands: 18
13ExprTuple19
14Literal
15ExprTuple20
16ExprTuple31, 21
17Literal
18ExprTuple30, 21
19Operationoperator: 23
operands: 22
20Operationoperator: 23
operands: 24
21Literal
22ExprTuple31, 25
23Literal
24ExprTuple30, 26
25Operationoperator: 28
operand: 30
26Operationoperator: 28
operand: 31
27ExprTuple30
28Literal
29ExprTuple31
30Variable
31Variable