Expression of type Lambda

from the theory of proveit.numbers.division

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, c, d, e
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Mult, frac

# build up the expression from sub-expressions
expr = Lambda([b, c, e], Conditional(Equals(Mult(frac(a, Mult(b, c)), frac(Mult(c, d), e)), Mult(frac(a, b), frac(d, e))), And(InSet(b, ComplexNonZero), InSet(c, ComplexNonZero), InSet(e, ComplexNonZero))))

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(b, c, e\right) \mapsto \left\{\left(\frac{a}{b \cdot c} \cdot \frac{c \cdot d}{e}\right) = \left(\frac{a}{b} \cdot \frac{d}{e}\right) \textrm{ if } b \in \mathbb{C}^{\neq 0} ,  c \in \mathbb{C}^{\neq 0} ,  e \in \mathbb{C}^{\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	37, 38, 33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 35 operands: 14
10	Operation	operator: 35 operands: 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	20, 21
15	ExprTuple	22, 23
16	ExprTuple	37, 24
17	ExprTuple	38, 24
18	Literal
19	ExprTuple	33, 24
20	Operation	operator: 28 operands: 25
21	Operation	operator: 28 operands: 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	Literal
25	ExprTuple	32, 30
26	ExprTuple	31, 33
27	ExprTuple	32, 37
28	Literal
29	ExprTuple	39, 33
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	Variable
33	Variable
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Variable
39	Variable