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, n
from proveit.core_expr_types import Len, f_1_to_n
from proveit.core_expr_types.tuples import f_1_to_i__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], Conditional(Equals(Len(operands = [f_1_to_i__1_to_n]), Mult(n, i)).with_wrapping_at(1), InSet(i, 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\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(1\right), f_{1}\left(2\right), \ldots, f_{1}\left(i\right), f_{2}\left(1\right), f_{2}\left(2\right), \ldots, f_{2}\left(i\right), \ldots\ldots, f_{n}\left(1\right), f_{n}\left(2\right), \ldots, f_{n}\left(i\right)\right)| \\  = \left(n \cdot i\right) \end{array} \end{array} \textrm{ if } i \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, 25
2	Conditional	value: 4 condition: 5
3	ExprRange	lambda_map: 6 start_index: 24 end_index: 21
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	Lambda	parameter: 31 body: 11
7	Literal
8	ExprTuple	12, 13
9	Literal
10	ExprTuple	25, 14
11	IndexedVar	variable: 29 index: 31
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	21, 25
19	ExprRange	lambda_map: 20 start_index: 24 end_index: 21
20	Lambda	parameter: 32 body: 22
21	Variable
22	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
23	Lambda	parameter: 31 body: 26
24	Literal
25	Variable
26	Operation	operator: 27 operand: 31
27	IndexedVar	variable: 29 index: 32
28	ExprTuple	31
29	Variable
30	ExprTuple	32
31	Variable
32	Variable