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

# build up the expression from sub-expressions
sub_expr1 = TensorProd(x, fi, y)
expr = Lambda(i, Conditional(Equals(ScalarMult(gamma, ScalarMult(beta, sub_expr1)), ScalarMult(ScalarMult(gamma, beta), sub_expr1)), 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(\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) \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: 32 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	32, 10
8	Operation	operator: 20 operands: 11
9	Operation	operator: 20 operands: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	23, 15
12	ExprTuple	16, 22
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	24, 22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 25 operands: 26
23	Variable
24	Variable
25	Literal
26	ExprTuple	27, 28, 29
27	Variable
28	Operation	operator: 30 operand: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable