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, 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(Mult(w_1_to_m, frac(x, y), z_1_to_n), 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\{\left(w_{1} \cdot  w_{2} \cdot  \ldots \cdot  w_{m} \cdot \frac{x}{y}\cdot z_{1} \cdot  z_{2} \cdot  \ldots \cdot  z_{n}\right) = \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} \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	37, 38, 36, 39
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: 31 operands: 16
10	Operation	operator: 29 operands: 17
11	ExprRange	lambda_map: 18 start_index: 44 end_index: 42
12	Operation	operator: 34 operands: 19
13	Operation	operator: 34 operands: 20
14	ExprRange	lambda_map: 21 start_index: 44 end_index: 45
15	Operation	operator: 22 operands: 23
16	ExprTuple	37, 24, 39
17	ExprTuple	25, 36
18	Lambda	parameter: 51 body: 26
19	ExprTuple	38, 40
20	ExprTuple	36, 40
21	Lambda	parameter: 51 body: 27
22	Literal
23	ExprTuple	36, 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 31 operands: 32
26	Operation	operator: 34 operands: 33
27	Operation	operator: 34 operands: 35
28	Literal
29	Literal
30	ExprTuple	38, 36
31	Literal
32	ExprTuple	37, 38, 39
33	ExprTuple	46, 40
34	Literal
35	ExprTuple	47, 40
36	Variable
37	ExprRange	lambda_map: 41 start_index: 44 end_index: 42
38	Variable
39	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
40	Literal
41	Lambda	parameter: 51 body: 46
42	Variable
43	Lambda	parameter: 51 body: 47
44	Literal
45	Variable
46	IndexedVar	variable: 48 index: 51
47	IndexedVar	variable: 49 index: 51
48	Variable
49	Variable
50	ExprTuple	51
51	Variable