Expression of type Conditional ¶

from the theory of proveit.numbers.multiplication ¶

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, b, i, j
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, Mult, Natural, Neg

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_j], instance_expr = Equals(Neg(Mult(a_1_to_i, Neg(b), c_1_to_j)), Mult(a_1_to_i, b, c_1_to_j)), domain = Complex), And(InSet(i, Natural), InSet(j, Natural)))

# 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_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{j} \in \mathbb{C}}~\left(\left(-\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(-b\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right)\right) = \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{j}\right)\right) \textrm{ if } i \in \mathbb{N} ,  j \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: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 25 body: 9
7	Operation	operator: 35 operands: 10
8	Operation	operator: 35 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	42, 14
11	ExprTuple	47, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	Operation	operator: 43 operand: 29
20	Operation	operator: 32 operands: 25
21	ExprRange	lambda_map: 26 start_index: 46 end_index: 42
22	Operation	operator: 35 operands: 27
23	ExprRange	lambda_map: 28 start_index: 46 end_index: 47
24	ExprTuple	29
25	ExprTuple	37, 49, 39
26	Lambda	parameter: 54 body: 30
27	ExprTuple	49, 40
28	Lambda	parameter: 54 body: 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 35 operands: 34
31	Operation	operator: 35 operands: 36
32	Literal
33	ExprTuple	37, 38, 39
34	ExprTuple	48, 40
35	Literal
36	ExprTuple	50, 40
37	ExprRange	lambda_map: 41 start_index: 46 end_index: 42
38	Operation	operator: 43 operand: 49
39	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
40	Literal
41	Lambda	parameter: 54 body: 48
42	Variable
43	Literal
44	ExprTuple	49
45	Lambda	parameter: 54 body: 50
46	Literal
47	Variable
48	IndexedVar	variable: 51 index: 54
49	Variable
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.multiplication¶

Expression of type Conditional ¶

from the theory of proveit.numbers.multiplication ¶