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, fi, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Interval, four, two

# build up the expression from sub-expressions
sub_expr1 = Interval(two, four)
sub_expr2 = TensorProd(x, fi, y)
sub_expr3 = InSet(i, sub_expr1)
sub_expr4 = ScalarMult(ScalarMult(gamma, beta), sub_expr2)
sub_expr5 = ScalarMult(gamma, ScalarMult(beta, sub_expr2))
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_expr3)), Lambda(i, Conditional(sub_expr4, sub_expr3))).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(\beta \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right)\right) = \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right)\right), \begin{array}{c} \begin{array}{l} \left[i \mapsto \left\{\gamma \cdot \left(\beta \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] =  \\ \left[i \mapsto \left\{\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\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: 14 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 42 body: 9
7	Lambda	parameter: 42 body: 10
8	Lambda	parameter: 42 body: 11
9	Conditional	value: 12 condition: 13
10	Conditional	value: 18 condition: 13
11	Conditional	value: 19 condition: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	42, 20
18	Operation	operator: 30 operands: 21
19	Operation	operator: 30 operands: 22
20	Operation	operator: 23 operands: 24
21	ExprTuple	33, 25
22	ExprTuple	26, 32
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 30 operands: 29
26	Operation	operator: 30 operands: 31
27	Literal
28	Literal
29	ExprTuple	34, 32
30	Literal
31	ExprTuple	33, 34
32	Operation	operator: 35 operands: 36
33	Variable
34	Variable
35	Literal
36	ExprTuple	37, 38, 39
37	Variable
38	Operation	operator: 40 operand: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable