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 Equals, Forall, InSet
from proveit.numbers import Add, NaturalPos, one

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

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())

n \mapsto \left\{\forall_{x_{1}, x_{2}, \ldots, x_{n + 1}~|~\left(x_{1} = x_{1 + 1}\right), \left(x_{2} = x_{2 + 1}\right), \ldots, \left(x_{n} = x_{n + 1}\right)}~\left(x_{1} = x_{n + 1}\right) \textrm{ if } n \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	parameter: 31 body: 2
1	ExprTuple	31
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	31, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	13
12	Conditional	value: 14 condition: 15
13	ExprRange	lambda_map: 16 start_index: 41 end_index: 26
14	Operation	operator: 29 operands: 17
15	Operation	operator: 18 operands: 19
16	Lambda	parameter: 40 body: 32
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	IndexedVar	variable: 35 index: 41
21	IndexedVar	variable: 35 index: 26
22	ExprRange	lambda_map: 25 start_index: 41 end_index: 31
23	ExprTuple	41
24	ExprTuple	26
25	Lambda	parameter: 40 body: 27
26	Operation	operator: 38 operands: 28
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 41
29	Literal
30	ExprTuple	32, 33
31	Variable
32	IndexedVar	variable: 35 index: 40
33	IndexedVar	variable: 35 index: 37
34	ExprTuple	40
35	Variable
36	ExprTuple	37
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
40	Variable
41	Literal