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

# build up the expression from sub-expressions
expr = Lambda(i, Conditional(Equals(TensorProd(x, y, fi, z), TensorProd(x, TensorProd(y, fi), z)), 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(x {\otimes} y {\otimes} f\left(i\right) {\otimes} z\right) = \left(x {\otimes} \left(y {\otimes} f\left(i\right)\right) {\otimes} z\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: 26 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	26, 10
8	Operation	operator: 20 operands: 11
9	Operation	operator: 20 operands: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	15, 22, 23, 17
12	ExprTuple	15, 16, 17
13	Literal
14	ExprTuple	18, 19
15	Variable
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	Literal
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Operation	operator: 24 operand: 26
24	Variable
25	ExprTuple	26
26	Variable