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, x
from proveit.core_expr_types import Len, f_1_to_i, range_1_to_ip1
from proveit.logic import Equals, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Equals(Len(operands = [f_1_to_i, x]), Len(operands = [range_1_to_ip1])), 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\{|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right), x\right)| = |\left(1, 2, \ldots, \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 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	24, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15
13	ExprRange	lambda_map: 16 start_index: 25 end_index: 24
14	Variable
15	ExprRange	lambda_map: 17 start_index: 25 end_index: 18
16	Lambda	parameter: 26 body: 19
17	Lambda	parameter: 26 body: 26
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operand: 26
20	Literal
21	ExprTuple	24, 25
22	Variable
23	ExprTuple	26
24	Variable
25	Literal
26	Variable