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 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 Equals, Forall, 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([m, n], Forall(instance_param_or_params = [w_1_to_m, x, y, z_1_to_n], instance_expr = 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)))), domain = Complex, conditions = [NotEquals(y, zero), ExprRange(sub_expr1, NotEquals(IndexedVar(w, sub_expr1), zero), one, m), ExprRange(sub_expr1, NotEquals(IndexedVar(z, sub_expr1), 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(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(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)}~\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)\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	60, 63
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	56, 48, 57, 58
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18, 19, 20, 21, 22
14	Operation	operator: 39 operands: 23
15	Operation	operator: 52 operand: 33
16	ExprRange	lambda_map: 25 start_index: 62 end_index: 60
17	Operation	operator: 42 operands: 26
18	Operation	operator: 42 operands: 27
19	ExprRange	lambda_map: 28 start_index: 62 end_index: 63
20	Operation	operator: 45 operands: 29
21	ExprRange	lambda_map: 30 start_index: 62 end_index: 60
22	ExprRange	lambda_map: 31 start_index: 62 end_index: 63
23	ExprTuple	48, 32
24	ExprTuple	33
25	Lambda	parameter: 69 body: 34
26	ExprTuple	48, 50
27	ExprTuple	57, 50
28	Lambda	parameter: 69 body: 35
29	ExprTuple	57, 51
30	Lambda	parameter: 69 body: 36
31	Lambda	parameter: 69 body: 37
32	Operation	operator: 54 operands: 38
33	Operation	operator: 39 operands: 40
34	Operation	operator: 42 operands: 41
35	Operation	operator: 42 operands: 43
36	Operation	operator: 45 operands: 44
37	Operation	operator: 45 operands: 46
38	ExprTuple	56, 47, 58
39	Literal
40	ExprTuple	48, 49
41	ExprTuple	64, 50
42	Literal
43	ExprTuple	65, 50
44	ExprTuple	64, 51
45	Literal
46	ExprTuple	65, 51
47	Operation	operator: 52 operand: 57
48	Variable
49	Operation	operator: 54 operands: 55
50	Literal
51	Literal
52	Literal
53	ExprTuple	57
54	Literal
55	ExprTuple	56, 57, 58
56	ExprRange	lambda_map: 59 start_index: 62 end_index: 60
57	Variable
58	ExprRange	lambda_map: 61 start_index: 62 end_index: 63
59	Lambda	parameter: 69 body: 64
60	Variable
61	Lambda	parameter: 69 body: 65
62	Literal
63	Variable
64	IndexedVar	variable: 66 index: 69
65	IndexedVar	variable: 67 index: 69
66	Variable
67	Variable
68	ExprTuple	69
69	Variable