Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 31 body: 3
2	ExprTuple	31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 19 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	31, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	13, 35
12	Conditional	value: 14 condition: 15
13	ExprRange	lambda_map: 16 start_index: 34 end_index: 31
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Lambda	parameter: 41 body: 21
17	Literal
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	35, 24
21	IndexedVar	variable: 39 index: 41
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	31, 35
29	ExprRange	lambda_map: 30 start_index: 34 end_index: 31
30	Lambda	parameter: 42 body: 32
31	Variable
32	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
33	Lambda	parameter: 41 body: 36
34	Literal
35	Variable
36	Operation	operator: 37 operand: 41
37	IndexedVar	variable: 39 index: 42
38	ExprTuple	41
39	Variable
40	ExprTuple	42
41	Variable
42	Variable