Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3	,  ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	,  ⊢
	: , : , :
3	instantiation	6, 18, 7	,  ⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 9, 32, 10, 11, 12, 13, 14, 15	,  ⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.rounding.ceil_of_real_plus_int
7	instantiation	16, 25, 27	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.association
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	instantiation	17	⊢
	: , :
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	30, 20, 18	⊢
	: , : , :
14	instantiation	30, 20, 19	⊢
	: , : , :
15	instantiation	30, 20, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	assumption		⊢
19	instantiation	30, 23, 22	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
21	instantiation	30, 23, 24	⊢
	: , : , :
22	instantiation	30, 26, 25	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
24	instantiation	30, 26, 27	⊢
	: , : , :
25	instantiation	28, 29	⊢
	:
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
27	instantiation	30, 31, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.negation.int_closure
29	assumption		⊢
30	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
31	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2