Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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