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, Forall, InSet
from proveit.numbers import Mult, Natural, NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [f_1_to_n, i], instance_expr = Equals(Len(operands = [f_1_to_i__1_to_n]), Mult(n, i)).with_wrapping_at(1), condition = InSet(i, Natural)), InSet(n, NaturalPos)))

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())

n \mapsto \left\{\forall_{f_{1}, f_{2}, \ldots, f_{n}, i~|~i \in \mathbb{N}}~\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}\right) \textrm{ if } n \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	parameter: 30 body: 2
1	ExprTuple	30
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 18 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	30, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	12, 34
11	Conditional	value: 13 condition: 14
12	ExprRange	lambda_map: 15 start_index: 33 end_index: 30
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Lambda	parameter: 40 body: 20
16	Literal
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	34, 23
20	IndexedVar	variable: 38 index: 40
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operands: 27
23	Literal
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	30, 34
28	ExprRange	lambda_map: 29 start_index: 33 end_index: 30
29	Lambda	parameter: 41 body: 31
30	Variable
31	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
32	Lambda	parameter: 40 body: 35
33	Literal
34	Variable
35	Operation	operator: 36 operand: 40
36	IndexedVar	variable: 38 index: 41
37	ExprTuple	40
38	Variable
39	ExprTuple	41
40	Variable
41	Variable