Expression of type Lambda

from the theory of proveit.core_expr_types.tuples

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, i, j, n
from proveit.core_expr_types import Len, f_1_to_n, i_to_j_len
from proveit.core_expr_types.tuples import f_i_to_j__1_to_n
from proveit.logic import Equals, InSet
from proveit.numbers import Mult, Natural

# build up the expression from sub-expressions
expr = Lambda([f_1_to_n, i, j], Conditional(Equals(Len(operands = [f_i_to_j__1_to_n]), Mult(n, i_to_j_len)).with_wrapping_at(1), InSet(i_to_j_len, Natural)))

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(f_{1}, f_{2}, \ldots, f_{n}, i, j\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(i\right), f_{1}\left(i + 1\right), \ldots, f_{1}\left(j\right), f_{2}\left(i\right), f_{2}\left(i + 1\right), \ldots, f_{2}\left(j\right), \ldots\ldots, f_{n}\left(i\right), f_{n}\left(i + 1\right), \ldots, f_{n}\left(j\right)\right)| \\  = \left(n \cdot \left(j - i + 1\right)\right) \end{array} \end{array} \textrm{ if } \left(j - i + 1\right) \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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