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, f, i, x
from proveit.core_expr_types import Len, f_1_to_i
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Natural, one

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f, x], instance_expr = Equals(Len(operands = [f_1_to_i, x]), 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_{f, x}~\left(|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right), x\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	23, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	25, 20
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	23, 22
19	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
20	Variable
21	Lambda	parameter: 27 body: 24
22	Literal
23	Variable
24	Operation	operator: 25 operand: 27
25	Variable
26	ExprTuple	27
27	Variable