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 x, y
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, Mult, subtract

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, x, y, b_1_to_j], instance_expr = Equals(Mult(a_1_to_i, subtract(x, y), b_1_to_j), subtract(Mult(a_1_to_i, x, b_1_to_j), Mult(a_1_to_i, y, b_1_to_j))).with_wrapping_at(2), domain = Complex)

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())

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

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('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	44, 37, 45, 46
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, 17
12	Operation	operator: 42 operands: 18
13	Operation	operator: 29 operands: 19
14	ExprRange	lambda_map: 20 start_index: 50 end_index: 48
15	Operation	operator: 34 operands: 21
16	Operation	operator: 34 operands: 22
17	ExprRange	lambda_map: 23 start_index: 50 end_index: 51
18	ExprTuple	44, 24, 46
19	ExprTuple	25, 26
20	Lambda	parameter: 57 body: 27
21	ExprTuple	37, 39
22	ExprTuple	45, 39
23	Lambda	parameter: 57 body: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 42 operands: 31
26	Operation	operator: 40 operand: 38
27	Operation	operator: 34 operands: 33
28	Operation	operator: 34 operands: 35
29	Literal
30	ExprTuple	37, 36
31	ExprTuple	44, 37, 46
32	ExprTuple	38
33	ExprTuple	52, 39
34	Literal
35	ExprTuple	53, 39
36	Operation	operator: 40 operand: 45
37	Variable
38	Operation	operator: 42 operands: 43
39	Literal
40	Literal
41	ExprTuple	45
42	Literal
43	ExprTuple	44, 45, 46
44	ExprRange	lambda_map: 47 start_index: 50 end_index: 48
45	Variable
46	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
47	Lambda	parameter: 57 body: 52
48	Variable
49	Lambda	parameter: 57 body: 53
50	Literal
51	Variable
52	IndexedVar	variable: 54 index: 57
53	IndexedVar	variable: 55 index: 57
54	Variable
55	Variable
56	ExprTuple	57
57	Variable