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Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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, Or
from proveit.numbers import Complex, Mult, ZeroSet, zero
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(InSet(Mult(a, b), ZeroSet), And(InSet(a, Complex), InSet(b, Complex), Or(Equals(a, zero), Equals(b, zero))))))
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 \cdot b\right) \in \left\{0\right\} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  \left(a = 0\right) \lor \left(b = 0\right)\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: 14
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 18
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12
8Operationoperator: 13
operands: 14
9Operationoperator: 15
operand: 30
10Operationoperator: 18
operands: 17
11Operationoperator: 18
operands: 19
12Operationoperator: 20
operands: 21
13Literal
14ExprTuple28, 29
15Literal
16ExprTuple30
17ExprTuple28, 22
18Literal
19ExprTuple29, 22
20Literal
21ExprTuple23, 24
22Literal
23Operationoperator: 26
operands: 25
24Operationoperator: 26
operands: 27
25ExprTuple28, 30
26Literal
27ExprTuple29, 30
28Variable
29Variable
30Literal