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, f, i
from proveit.core_expr_types import Len, f_1_to_i, range_1_to_i
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(i, Conditional(Forall(instance_param_or_params = [f], instance_expr = Equals(Len(operands = [f_1_to_i]), Len(operands = [range_1_to_i]))), 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_{f}~\left(|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right)\right)| = |\left(1, 2, \ldots, i\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: 26 body: 3
2	ExprTuple	26
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	26, 11
10	Lambda	parameter: 28 body: 13
11	Literal
12	ExprTuple	28
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	ExprRange	lambda_map: 23 start_index: 25 end_index: 26
22	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
23	Lambda	parameter: 30 body: 27
24	Lambda	parameter: 30 body: 30
25	Literal
26	Variable
27	Operation	operator: 28 operand: 30
28	Variable
29	ExprTuple	30
30	Variable