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, 4, 5	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.division.strong_div_from_denom_bound__all_pos
2	instantiation	45, 8, 6	⊢
	: , : , :
3	instantiation	45, 8, 7	⊢
	: , : , :
4	instantiation	45, 8, 9	⊢
	: , : , :
5	instantiation	10, 11, 41, 12, 13, 14	⊢
	: , : , :
6	instantiation	45, 16, 44	⊢
	: , : , :
7	instantiation	45, 16, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
9	instantiation	45, 16, 17	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less
11	instantiation	45, 29, 18	⊢
	: , : , :
12	instantiation	45, 29, 19	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
14	instantiation	20, 41, 21, 22, 23, 24*	⊢
	: , : , :
15	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
16	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
17	instantiation	25, 35, 26	⊢
	: , :
18	instantiation	45, 38, 27	⊢
	: , : , :
19	instantiation	45, 38, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
22	instantiation	45, 29, 30	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
24	instantiation	31, 32	⊢
	:
25	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
26	instantiation	33, 47, 34	⊢
	: , :
27	instantiation	45, 46, 35	⊢
	: , : , :
28	instantiation	45, 36, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	45, 38, 39	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.elim_zero_left
32	instantiation	45, 40, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
34	instantiation	45, 42, 50	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
37	instantiation	43, 44, 50	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	45, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	48, 49, 50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
43	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
48	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
49	instantiation	51, 52	⊢
	: , :
50	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
51	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements