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 ExprTuple, Lambda, f, i, j, x
from proveit.core_expr_types import Len, f_i_to_j
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Natural, Neg, two

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, x], Forall(instance_param_or_params = [i, j], instance_expr = Equals(Len(operands = [f_i_to_j, x]), Add(j, Neg(i), two)), condition = InSet(Len(operands = [f_i_to_j]), 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(\left(f, x\right) \mapsto \left[\forall_{i, j~|~|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}}~\left(|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = \left(j - i + 2\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	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	34, 24
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 7 body: 8
7	ExprTuple	32, 31
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operands: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 22 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	ExprTuple	27, 24
20	Literal
21	ExprTuple	31, 25, 26
22	Literal
23	ExprTuple	27
24	Variable
25	Operation	operator: 28 operand: 32
26	Literal
27	ExprRange	lambda_map: 30 start_index: 32 end_index: 31
28	Literal
29	ExprTuple	32
30	Lambda	parameter: 36 body: 33
31	Variable
32	Variable
33	Operation	operator: 34 operand: 36
34	Variable
35	ExprTuple	36
36	Variable