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
from proveit.core_expr_types import merge_series_conditions, merge_series_equiv, x_0_to_jmi
from proveit.logic import And

# build up the expression from sub-expressions
expr = Lambda([x_0_to_jmi], Conditional(merge_series_equiv, And(merge_series_conditions)))

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(x_{0}, x_{1}, \ldots, x_{j - i}\right) \mapsto \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} \textrm{ if } \left(x_{0} = f\left(i + 0\right)\right) \land  \left(x_{1} = f\left(i + 1\right)\right) \land  \ldots \land  \left(x_{j - i} = f\left(i + \left(j - i\right)\right)\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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