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 i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Add, Interval, Mult, Real, four, one, three, two

# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
expr = Forall(instance_param_or_params = [i], instance_expr = InSet(TensorProd(x, ScalarMult(Mult(i, Add(i, one)), y)), TensorProd(sub_expr1, sub_expr1)), 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(\left(x {\otimes} \left(\left(i \cdot \left(i + 1\right)\right) \cdot y\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\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: 37 body: 5
4	ExprTuple	37
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	37, 13
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 21
17	Literal
18	ExprTuple	22, 23
19	Variable
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operands: 33
29	Variable
30	Literal
31	Literal
32	Literal
33	ExprTuple	37, 34
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37, 38
37	Variable
38	Literal