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, b, i
from proveit.core_expr_types import Len, a_1_to_i
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Natural, one

# build up the expression from sub-expressions
sub_expr1 = [a_1_to_i, b]
expr = Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Len(operands = sub_expr1), Add(i, one))), 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\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b}~\left(|\left(a_{1}, a_{2}, \ldots, a_{i}, b\right)| = \left(i + 1\right)\right) \textrm{ if } i \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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	22, 8
7	Lambda	parameters: 15 body: 9
8	Literal
9	Operation	operator: 10 operands: 11
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	22, 21
18	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
19	Variable
20	Lambda	parameter: 26 body: 23
21	Literal
22	Variable
23	IndexedVar	variable: 24 index: 26
24	Variable
25	ExprTuple	26
26	Variable