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, ExprRange, IndexedVar, Lambda, Variable, m, n, w, x, y, z
from proveit.core_expr_types import w_1_to_m, z_1_to_n
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Mult, Neg, frac, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(w, sub_expr1)
sub_expr3 = IndexedVar(z, sub_expr1)
expr = Lambda([w_1_to_m, x, y, z_1_to_n], Conditional(Equals(frac(x, Mult(w_1_to_m, Neg(y), z_1_to_n)), Neg(frac(x, Mult(w_1_to_m, y, z_1_to_n)))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, m), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(sub_expr3, Complex), one, n), NotEquals(y, zero), ExprRange(sub_expr1, NotEquals(sub_expr2, zero), one, m), ExprRange(sub_expr1, NotEquals(sub_expr3, zero), one, n))))

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(w_{1}, w_{2}, \ldots, w_{m}, x, y, z_{1}, z_{2}, \ldots, z_{n}\right) \mapsto \left\{\frac{x}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \left(-y\right)\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}} = \left(-\frac{x}{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot y\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}\right) \textrm{ if } \left(w_{1} \in \mathbb{C}\right) ,  \left(w_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(w_{m} \in \mathbb{C}\right) ,  x \in \mathbb{C} ,  y \in \mathbb{C}, \left(z_{1} \in \mathbb{C}\right) ,  \left(z_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(z_{n} \in \mathbb{C}\right) ,  y \neq 0, \left(w_{1} \neq 0\right) ,  \left(w_{2} \neq 0\right) ,  \ldots ,  \left(w_{m} \neq 0\right), \left(z_{1} \neq 0\right) ,  \left(z_{2} \neq 0\right) ,  \ldots ,  \left(z_{n} \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	Lambda	parameters: 1 body: 2
1	ExprTuple	51, 43, 52, 53
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, 14, 15, 16, 17
9	Operation	operator: 34 operands: 18
10	Operation	operator: 47 operand: 28
11	ExprRange	lambda_map: 20 start_index: 57 end_index: 55
12	Operation	operator: 37 operands: 21
13	Operation	operator: 37 operands: 22
14	ExprRange	lambda_map: 23 start_index: 57 end_index: 58
15	Operation	operator: 40 operands: 24
16	ExprRange	lambda_map: 25 start_index: 57 end_index: 55
17	ExprRange	lambda_map: 26 start_index: 57 end_index: 58
18	ExprTuple	43, 27
19	ExprTuple	28
20	Lambda	parameter: 64 body: 29
21	ExprTuple	43, 45
22	ExprTuple	52, 45
23	Lambda	parameter: 64 body: 30
24	ExprTuple	52, 46
25	Lambda	parameter: 64 body: 31
26	Lambda	parameter: 64 body: 32
27	Operation	operator: 49 operands: 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 37 operands: 36
30	Operation	operator: 37 operands: 38
31	Operation	operator: 40 operands: 39
32	Operation	operator: 40 operands: 41
33	ExprTuple	51, 42, 53
34	Literal
35	ExprTuple	43, 44
36	ExprTuple	59, 45
37	Literal
38	ExprTuple	60, 45
39	ExprTuple	59, 46
40	Literal
41	ExprTuple	60, 46
42	Operation	operator: 47 operand: 52
43	Variable
44	Operation	operator: 49 operands: 50
45	Literal
46	Literal
47	Literal
48	ExprTuple	52
49	Literal
50	ExprTuple	51, 52, 53
51	ExprRange	lambda_map: 54 start_index: 57 end_index: 55
52	Variable
53	ExprRange	lambda_map: 56 start_index: 57 end_index: 58
54	Lambda	parameter: 64 body: 59
55	Variable
56	Lambda	parameter: 64 body: 60
57	Literal
58	Variable
59	IndexedVar	variable: 61 index: 64
60	IndexedVar	variable: 62 index: 64
61	Variable
62	Variable
63	ExprTuple	64
64	Variable