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, x, y, z
from proveit.logic import Equals, InSet
from proveit.numbers import Complex, Mult, frac

# build up the expression from sub-expressions
expr = Lambda(y, Conditional(Equals(frac(Mult(y, x), Mult(z, x)), frac(y, z)), InSet(y, Complex)))

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())

y \mapsto \left\{\frac{y \cdot x}{z \cdot x} = \frac{y}{z} \textrm{ if } y \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 20 body: 2
1	ExprTuple	20
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	20, 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	20, 21
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 22
18	Literal
19	ExprTuple	21, 22
20	Variable
21	Variable
22	Variable