Expression of type ExprTuple

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, ExprTuple, Lambda, f, 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 = ExprTuple(Lambda([f, i, j], 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(\left(f, i, j\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	41, 46, 33
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	26, 11
10	Lambda	parameters: 18 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 31 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	ExprTuple	21
19	ExprTuple	22
20	ExprRange	lambda_map: 23 start_index: 25 end_index: 26
21	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
22	ExprRange	lambda_map: 27 start_index: 46 end_index: 33
23	Lambda	parameter: 47 body: 28
24	Lambda	parameter: 47 body: 35
25	Literal
26	Operation	operator: 44 operands: 29
27	Lambda	parameter: 47 body: 30
28	Operation	operator: 31 operands: 32
29	ExprTuple	33, 34
30	Operation	operator: 41 operand: 47
31	Literal
32	ExprTuple	35, 36
33	Variable
34	Operation	operator: 37 operand: 46
35	IndexedVar	variable: 39 index: 47
36	Operation	operator: 41 operand: 43
37	Literal
38	ExprTuple	46
39	Variable
40	ExprTuple	47
41	Variable
42	ExprTuple	43
43	Operation	operator: 44 operands: 45
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Variable