Expression of type Forall

from the theory of proveit.linear_algebra.tensors

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 beta, gamma, i
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, Mult, four, one, two

# build up the expression from sub-expressions
sub_expr1 = Add(i, one)
expr = Forall(instance_param_or_params = [i], instance_expr = Equals(Mult(gamma, beta, i, sub_expr1), Mult(Mult(gamma, beta), i, sub_expr1)).with_wrapping_at(2), domain = Interval(two, four))

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_{i \in \{2~\ldotp \ldotp~4\}}~\left(\begin{array}{c} \begin{array}{l} \left(\gamma \cdot \beta \cdot i \cdot \left(i + 1\right)\right) =  \\ \left(\left(\gamma \cdot \beta\right) \cdot i \cdot \left(i + 1\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	parameter: 29 body: 5
4	ExprTuple	29
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	29, 14
12	Operation	operator: 23 operands: 15
13	Operation	operator: 23 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	27, 28, 29, 20
16	ExprTuple	19, 29, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	Literal
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30
27	Variable
28	Variable
29	Variable
30	Literal