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Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple32, 31
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13
10Operationoperator: 15
operand: 20
11Operationoperator: 15
operand: 21
12Operationoperator: 18
operands: 17
13Operationoperator: 18
operands: 19
14ExprTuple20
15Literal
16ExprTuple21
17ExprTuple32, 22
18Literal
19ExprTuple31, 22
20Operationoperator: 24
operands: 23
21Operationoperator: 24
operands: 25
22Literal
23ExprTuple32, 26
24Literal
25ExprTuple31, 27
26Operationoperator: 29
operand: 31
27Operationoperator: 29
operand: 32
28ExprTuple31
29Literal
30ExprTuple32
31Variable
32Variable