Expression of type Conditional ¶

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, 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 = 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)))

# 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\{\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()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 45 operands: 11
8	Operation	operator: 45 operands: 12
9	ExprTuple	48, 49, 47, 50
10	Conditional	value: 13 condition: 14
11	ExprTuple	53, 15
12	ExprTuple	56, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24, 25, 26
20	Operation	operator: 42 operands: 27
21	Operation	operator: 40 operands: 28
22	ExprRange	lambda_map: 29 start_index: 55 end_index: 53
23	Operation	operator: 45 operands: 30
24	Operation	operator: 45 operands: 31
25	ExprRange	lambda_map: 32 start_index: 55 end_index: 56
26	Operation	operator: 33 operands: 34
27	ExprTuple	48, 35, 50
28	ExprTuple	36, 47
29	Lambda	parameter: 62 body: 37
30	ExprTuple	49, 51
31	ExprTuple	47, 51
32	Lambda	parameter: 62 body: 38
33	Literal
34	ExprTuple	47, 39
35	Operation	operator: 40 operands: 41
36	Operation	operator: 42 operands: 43
37	Operation	operator: 45 operands: 44
38	Operation	operator: 45 operands: 46
39	Literal
40	Literal
41	ExprTuple	49, 47
42	Literal
43	ExprTuple	48, 49, 50
44	ExprTuple	57, 51
45	Literal
46	ExprTuple	58, 51
47	Variable
48	ExprRange	lambda_map: 52 start_index: 55 end_index: 53
49	Variable
50	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
51	Literal
52	Lambda	parameter: 62 body: 57
53	Variable
54	Lambda	parameter: 62 body: 58
55	Literal
56	Variable
57	IndexedVar	variable: 59 index: 62
58	IndexedVar	variable: 60 index: 62
59	Variable
60	Variable
61	ExprTuple	62
62	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.division¶

Expression of type Conditional ¶

from the theory of proveit.numbers.division ¶