Expression of type ExprTuple

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 Conditional, ExprTuple, Lambda, beta, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Interval, four, one, two

# build up the expression from sub-expressions
sub_expr1 = Interval(two, four)
sub_expr2 = InSet(i, sub_expr1)
sub_expr3 = ScalarMult(beta, ScalarMult(Add(i, one), TensorProd(x, y)))
sub_expr4 = ScalarMult(ScalarMult(gamma, i), sub_expr3)
sub_expr5 = ScalarMult(gamma, ScalarMult(i, sub_expr3))
expr = ExprTuple(Forall(instance_param_or_params = [i], instance_expr = Equals(sub_expr5, sub_expr4), domain = sub_expr1), Equals(Lambda(i, Conditional(sub_expr5, sub_expr2)), Lambda(i, Conditional(sub_expr4, sub_expr2))).with_wrapping_at(2))

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())

\left(\forall_{i \in \{2~\ldotp \ldotp~4\}}~\left(\left(\gamma \cdot \left(i \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right)\right) = \left(\left(\gamma \cdot i\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right)\right), \begin{array}{c} \begin{array}{l} \left[i \mapsto \left\{\gamma \cdot \left(i \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] =  \\ \left[i \mapsto \left\{\left(\gamma \cdot i\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 45 body: 9
7	Lambda	parameter: 45 body: 10
8	Lambda	parameter: 45 body: 12
9	Conditional	value: 13 condition: 14
10	Conditional	value: 19 condition: 14
11	ExprTuple	45
12	Conditional	value: 20 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	45, 21
19	Operation	operator: 37 operands: 22
20	Operation	operator: 37 operands: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	33, 26
23	ExprTuple	27, 32
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 37 operands: 30
27	Operation	operator: 37 operands: 31
28	Literal
29	Literal
30	ExprTuple	45, 32
31	ExprTuple	33, 45
32	Operation	operator: 37 operands: 34
33	Variable
34	ExprTuple	35, 36
35	Variable
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Operation	operator: 41 operands: 42
40	Operation	operator: 43 operands: 44
41	Literal
42	ExprTuple	45, 46
43	Literal
44	ExprTuple	47, 48
45	Variable
46	Literal
47	Variable
48	Variable