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, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
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)
sub_expr2 = TensorProd(x, y)
expr = Forall(instance_param_or_params = [i], instance_expr = Equals(ScalarMult(ScalarMult(gamma, i), ScalarMult(beta, ScalarMult(sub_expr1, sub_expr2))), ScalarMult(Mult(gamma, i, beta, sub_expr1), sub_expr2)), 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(\left(\gamma \cdot i\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) = \left(\left(\gamma \cdot i \cdot \beta \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\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: 39 body: 5
4	ExprTuple	39
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	39, 14
12	Operation	operator: 31 operands: 15
13	Operation	operator: 31 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	19, 20
16	ExprTuple	21, 34
17	Literal
18	ExprTuple	22, 23
19	Operation	operator: 31 operands: 24
20	Operation	operator: 31 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Literal
24	ExprTuple	29, 39
25	ExprTuple	30, 28
26	Literal
27	ExprTuple	29, 39, 30, 33
28	Operation	operator: 31 operands: 32
29	Variable
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Variable
40	Literal
41	Variable
42	Variable