Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 33 operands: 12
8	Operation	operator: 33 operands: 13
9	Operation	operator: 16 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18, 19
13	ExprTuple	20, 21
14	ExprTuple	35, 22
15	ExprTuple	36, 22
16	Literal
17	ExprTuple	31, 22
18	Operation	operator: 26 operands: 23
19	Operation	operator: 26 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	30, 28
24	ExprTuple	29, 31
25	ExprTuple	30, 35
26	Literal
27	ExprTuple	37, 31
28	Operation	operator: 33 operands: 32
29	Operation	operator: 33 operands: 34
30	Variable
31	Variable
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Variable