Proof of proveit.numbers.numerals.decimals.tuple_len_5 theorem

import proveit
from proveit import a, b, e, i
from proveit.core_expr_types.tuples  import tuple_len_incr
from proveit.numbers.numerals.decimals import tuple_len_4, add_4_1
theory = proveit.Theory() # the theorem's theory

%proving tuple_len_5

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
tuple_len_5:
(see dependencies)

four_spec = tuple_len_4.instantiate({a:a}, auto_simplify=False)

four_spec:  ⊢  

tuple_spec = tuple_len_incr.instantiate(
    {i: four_spec.rhs, a: four_spec.lhs.operands, b: e})

tuple_spec:  ⊢  

tuple_len_5 may now be readily provable (assuming required theorems are usable).  Simply execute "%qed".

%qed

proveit.numbers.numerals.decimals.tuple_len_5 has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4, 5*	⊢
	: , : , :
2	axiom		⊢
	proveit.core_expr_types.tuples.tuple_len_incr
3	conjecture		⊢
	proveit.numbers.numerals.decimals.nat4
4	instantiation	6	⊢
	: , : , : , :
5	conjecture		⊢
	proveit.numbers.numerals.decimals.add_4_1
6	conjecture		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
*equality replacement requirements