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 Lambda, m, n, x, y
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, zero

# build up the expression from sub-expressions
expr = Lambda([m, n], Forall(instance_param_or_params = [w_1_to_m, x, y, z_1_to_n], instance_expr = 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))), domain = Complex, condition = 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(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(\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)\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	52, 55
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	48, 49, 42, 50
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
14	Operation	operator: 35 operands: 21
15	Operation	operator: 44 operand: 30
16	ExprRange	lambda_map: 23 start_index: 54 end_index: 52
17	Operation	operator: 38 operands: 24
18	Operation	operator: 38 operands: 25
19	ExprRange	lambda_map: 26 start_index: 54 end_index: 55
20	Operation	operator: 27 operands: 28
21	ExprTuple	29, 42
22	ExprTuple	30
23	Lambda	parameter: 61 body: 31
24	ExprTuple	49, 43
25	ExprTuple	42, 43
26	Lambda	parameter: 61 body: 32
27	Literal
28	ExprTuple	42, 33
29	Operation	operator: 46 operands: 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 38 operands: 37
32	Operation	operator: 38 operands: 39
33	Literal
34	ExprTuple	48, 40, 50
35	Literal
36	ExprTuple	41, 42
37	ExprTuple	56, 43
38	Literal
39	ExprTuple	57, 43
40	Operation	operator: 44 operand: 49
41	Operation	operator: 46 operands: 47
42	Variable
43	Literal
44	Literal
45	ExprTuple	49
46	Literal
47	ExprTuple	48, 49, 50
48	ExprRange	lambda_map: 51 start_index: 54 end_index: 52
49	Variable
50	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
51	Lambda	parameter: 61 body: 56
52	Variable
53	Lambda	parameter: 61 body: 57
54	Literal
55	Variable
56	IndexedVar	variable: 58 index: 61
57	IndexedVar	variable: 59 index: 61
58	Variable
59	Variable
60	ExprTuple	61
61	Variable