Expression of type Lambda

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, Lambda, beta, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import Equals, InSet
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 = Lambda(i, Conditional(Equals(ScalarMult(ScalarMult(gamma, i), ScalarMult(beta, ScalarMult(sub_expr1, sub_expr2))), ScalarMult(Mult(gamma, i, beta, sub_expr1), sub_expr2)), InSet(i, 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())

i \mapsto \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) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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