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}")
expr = Lambda([w_1_to_m, x, y, z_1_to_n], Conditional(Equals(frac(Mult(w_1_to_m, Neg(x), z_1_to_n), y), Neg(frac(Mult(w_1_to_m, x, z_1_to_n), y))), And(ExprRange(sub_expr1, InSet(IndexedVar(w, sub_expr1), Complex), one, m), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(IndexedVar(z, sub_expr1), Complex), one, n), NotEquals(y, 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(w_{1}, w_{2}, \ldots, w_{m}, x, y, z_{1}, z_{2}, \ldots, z_{n}\right) \mapsto \left\{\frac{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \left(-x\right)\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}{y} = \left(-\frac{w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot x\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}}{y}\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\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	43, 44, 37, 45
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
9	Operation	operator: 30 operands: 16
10	Operation	operator: 39 operand: 25
11	ExprRange	lambda_map: 18 start_index: 49 end_index: 47
12	Operation	operator: 33 operands: 19
13	Operation	operator: 33 operands: 20
14	ExprRange	lambda_map: 21 start_index: 49 end_index: 50
15	Operation	operator: 22 operands: 23
16	ExprTuple	24, 37
17	ExprTuple	25
18	Lambda	parameter: 56 body: 26
19	ExprTuple	44, 38
20	ExprTuple	37, 38
21	Lambda	parameter: 56 body: 27
22	Literal
23	ExprTuple	37, 28
24	Operation	operator: 41 operands: 29
25	Operation	operator: 30 operands: 31
26	Operation	operator: 33 operands: 32
27	Operation	operator: 33 operands: 34
28	Literal
29	ExprTuple	43, 35, 45
30	Literal
31	ExprTuple	36, 37
32	ExprTuple	51, 38
33	Literal
34	ExprTuple	52, 38
35	Operation	operator: 39 operand: 44
36	Operation	operator: 41 operands: 42
37	Variable
38	Literal
39	Literal
40	ExprTuple	44
41	Literal
42	ExprTuple	43, 44, 45
43	ExprRange	lambda_map: 46 start_index: 49 end_index: 47
44	Variable
45	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
46	Lambda	parameter: 56 body: 51
47	Variable
48	Lambda	parameter: 56 body: 52
49	Literal
50	Variable
51	IndexedVar	variable: 53 index: 56
52	IndexedVar	variable: 54 index: 56
53	Variable
54	Variable
55	ExprTuple	56
56	Variable