Expression of type ExprTuple

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, ExprTuple, Lambda, b, i
from proveit.core_expr_types import Len, a_1_to_i
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Natural, one

# build up the expression from sub-expressions
sub_expr1 = [a_1_to_i, b]
expr = ExprTuple(Lambda(i, Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Len(operands = sub_expr1), Add(i, one))), InSet(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(i \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b}~\left(|\left(a_{1}, a_{2}, \ldots, a_{i}, b\right)| = \left(i + 1\right)\right) \textrm{ if } i \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: 25 body: 3
2	ExprTuple	25
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	25, 11
10	Lambda	parameters: 18 body: 12
11	Literal
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	25, 24
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
22	Variable
23	Lambda	parameter: 29 body: 26
24	Literal
25	Variable
26	IndexedVar	variable: 27 index: 29
27	Variable
28	ExprTuple	29
29	Variable