Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\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	parameter: 32 body: 3
2	ExprTuple	32
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	32, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	14
13	Conditional	value: 15 condition: 16
14	ExprRange	lambda_map: 17 start_index: 42 end_index: 27
15	Operation	operator: 30 operands: 18
16	Operation	operator: 19 operands: 20
17	Lambda	parameter: 41 body: 33
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23
21	IndexedVar	variable: 36 index: 42
22	IndexedVar	variable: 36 index: 27
23	ExprRange	lambda_map: 26 start_index: 42 end_index: 32
24	ExprTuple	42
25	ExprTuple	27
26	Lambda	parameter: 41 body: 28
27	Operation	operator: 39 operands: 29
28	Operation	operator: 30 operands: 31
29	ExprTuple	32, 42
30	Literal
31	ExprTuple	33, 34
32	Variable
33	IndexedVar	variable: 36 index: 41
34	IndexedVar	variable: 36 index: 38
35	ExprTuple	41
36	Variable
37	ExprTuple	38
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Literal