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, m, n, x, y
from proveit.core_expr_types import w_1_to_m, z_1_to_n
from proveit.logic import And, Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Mult, NaturalPos, frac, zero

# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = [w_1_to_m, x, y, z_1_to_n], instance_expr = 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)), domain = Complex, condition = NotEquals(y, zero)), And(InSet(m, NaturalPos), InSet(n, NaturalPos))))

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(m, n\right) \mapsto \left\{\forall_{w_{1}, w_{2}, \ldots, w_{m}, x, y, z_{1}, z_{2}, \ldots, z_{n} \in \mathbb{C}~|~y \neq 0}~\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}\right) \textrm{ if } m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\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	55, 58
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 47 operands: 13
10	Operation	operator: 47 operands: 14
11	ExprTuple	50, 51, 49, 52
12	Conditional	value: 15 condition: 16
13	ExprTuple	55, 17
14	ExprTuple	58, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26, 27, 28
22	Operation	operator: 44 operands: 29
23	Operation	operator: 42 operands: 30
24	ExprRange	lambda_map: 31 start_index: 57 end_index: 55
25	Operation	operator: 47 operands: 32
26	Operation	operator: 47 operands: 33
27	ExprRange	lambda_map: 34 start_index: 57 end_index: 58
28	Operation	operator: 35 operands: 36
29	ExprTuple	50, 37, 52
30	ExprTuple	38, 49
31	Lambda	parameter: 64 body: 39
32	ExprTuple	51, 53
33	ExprTuple	49, 53
34	Lambda	parameter: 64 body: 40
35	Literal
36	ExprTuple	49, 41
37	Operation	operator: 42 operands: 43
38	Operation	operator: 44 operands: 45
39	Operation	operator: 47 operands: 46
40	Operation	operator: 47 operands: 48
41	Literal
42	Literal
43	ExprTuple	51, 49
44	Literal
45	ExprTuple	50, 51, 52
46	ExprTuple	59, 53
47	Literal
48	ExprTuple	60, 53
49	Variable
50	ExprRange	lambda_map: 54 start_index: 57 end_index: 55
51	Variable
52	ExprRange	lambda_map: 56 start_index: 57 end_index: 58
53	Literal
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