Show the Proof¶

In [1]:

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

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
2	instantiation	38, 6, 7	⊢
	: , : , :
3	instantiation	38, 9, 8	⊢
	: , : , :
4	instantiation	38, 9, 10	⊢
	: , : , :
5	instantiation	11, 32, 12, 13, 14, 15, 16^*	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
7	instantiation	38, 17, 33	⊢
	: , : , :
8	instantiation	38, 19, 18	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
10	instantiation	38, 19, 20	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
12	instantiation	38, 34, 21	⊢
	: , : , :
13	instantiation	22, 23, 25	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
15	instantiation	24, 25	⊢
	:
16	instantiation	26, 27	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
20	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
21	instantiation	38, 36, 28	⊢
	: , : , :
22	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
23	instantiation	29, 30	⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
25	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
26	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
27	instantiation	38, 31, 32	⊢
	: , : , :
28	instantiation	38, 39, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	38, 34, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	38, 36, 37	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	38, 39, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements