Expression of type Forall

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 ExprRange, IndexedVar, Variable, b, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k], instance_expr = Equals(Mult(a_1_to_i, Add(b_1_to_j), c_1_to_k), Add(ExprRange(sub_expr1, Mult(a_1_to_i, IndexedVar(b, sub_expr1), c_1_to_k), one, j))).with_wrapping_at(2), domain = Complex).with_wrapping()

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())

\begin{array}{l}\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k} \in \mathbb{C}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(b_{1} +  b_{2} +  \ldots +  b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{1}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{2}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) +  \ldots +  \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right)\right) \end{array} \end{array}\right)\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	True	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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