Expression of type Lambda

from the theory of proveit.logic.equality

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, ExprRange, IndexedVar, Lambda, Variable, n, x
from proveit.core_expr_types import x_1_to_np1
from proveit.logic import And, Equals
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([x_1_to_np1], Conditional(Equals(IndexedVar(x, one), IndexedVar(x, Add(n, one))), And(ExprRange(sub_expr1, Equals(IndexedVar(x, sub_expr1), IndexedVar(x, Add(sub_expr1, one))), one, n))))

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_{1}, x_{2}, \ldots, x_{n + 1}\right) \mapsto \left\{x_{1} = x_{n + 1} \textrm{ if } \left(x_{1} = x_{1 + 1}\right) \land  \left(x_{2} = x_{2 + 1}\right) \land  \ldots \land  \left(x_{n} = x_{n + 1}\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: 1 body: 2
1	ExprTuple	3
2	Conditional	value: 4 condition: 5
3	ExprRange	lambda_map: 6 start_index: 31 end_index: 16
4	Operation	operator: 19 operands: 7
5	Operation	operator: 8 operands: 9
6	Lambda	parameter: 30 body: 22
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12
10	IndexedVar	variable: 25 index: 31
11	IndexedVar	variable: 25 index: 16
12	ExprRange	lambda_map: 15 start_index: 31 end_index: 21
13	ExprTuple	31
14	ExprTuple	16
15	Lambda	parameter: 30 body: 17
16	Operation	operator: 28 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 31
19	Literal
20	ExprTuple	22, 23
21	Variable
22	IndexedVar	variable: 25 index: 30
23	IndexedVar	variable: 25 index: 27
24	ExprTuple	30
25	Variable
26	ExprTuple	27
27	Operation	operator: 28 operands: 29
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Literal