Expression of type ExprTuple

from the theory of proveit.numbers.divisibility

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, k
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Complex, Divides, Mult, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, k], Conditional(Divides(a, b), And(InSet(a, Complex), InSet(b, Complex), InSet(k, Complex), Divides(Mult(k, a), Mult(k, b)), NotEquals(k, zero)))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(a, b, k\right) \mapsto \left\{a \rvert b \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  k \in \mathbb{C} ,  \left(k \cdot a\right) \rvert \left(k \cdot b\right) ,  k \neq 0\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	29, 31, 30
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	29, 31
7	Literal
8	ExprTuple	9, 10, 11, 12, 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 20 operands: 21
14	ExprTuple	29, 22
15	ExprTuple	31, 22
16	Literal
17	ExprTuple	30, 22
18	Literal
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	30, 25
22	Literal
23	Operation	operator: 27 operands: 26
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable