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, j
from proveit.core_expr_types import merge_series_conditions, merge_series_equiv, x_0_to_jmi
from proveit.logic import Forall, InSet
from proveit.numbers import Natural, subtract

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x_0_to_jmi], instance_expr = merge_series_equiv, condition = merge_series_conditions), InSet(subtract(j, 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_{x_{0}, x_{1}, \ldots, x_{j - i}~|~\left(x_{0} = f\left(i + 0\right)\right), \left(x_{1} = f\left(i + 1\right)\right), \ldots, \left(x_{j - i} = f\left(i + \left(j - i\right)\right)\right)}~\left(\begin{array}{c} \begin{array}{l} \left(x_{0}, x_{1}, \ldots, x_{j - i}\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) \end{array} \end{array}\right) \textrm{ if } \left(j - i\right) \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: 15 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 28 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17
15	ExprTuple	18
16	ExprTuple	19
17	ExprRange	lambda_map: 20 start_index: 22 end_index: 23
18	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
19	ExprRange	lambda_map: 24 start_index: 43 end_index: 30
20	Lambda	parameter: 44 body: 25
21	Lambda	parameter: 44 body: 32
22	Literal
23	Operation	operator: 41 operands: 26
24	Lambda	parameter: 44 body: 27
25	Operation	operator: 28 operands: 29
26	ExprTuple	30, 31
27	Operation	operator: 38 operand: 44
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Operation	operator: 34 operand: 43
32	IndexedVar	variable: 36 index: 44
33	Operation	operator: 38 operand: 40
34	Literal
35	ExprTuple	43
36	Variable
37	ExprTuple	44
38	Variable
39	ExprTuple	40
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Variable
44	Variable