Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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