Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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