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Theorem Dependencies

proveit.numbers.summation.sum_first_n_int

see proof

In [1]:
import proveit
# Automation is not needed when querying dependencies:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
from proveit.numbers.summation import sum_first_n_int
In [2]:
%dependencies sum_first_n_int

Unproven conjectures required (directly or indirectly) to prove sum_first_n_int

proveit.core_expr_types.operations.operands_substitution_via_tuple
proveit.core_expr_types.tuples.extended_range_from1_len_typical_eq
proveit.core_expr_types.tuples.merge_extension
proveit.core_expr_types.tuples.range_from1_len_is_nat
proveit.core_expr_types.tuples.range_from1_len_typical_eq
proveit.core_expr_types.tuples.tuple_len_0_typical_eq
proveit.core_expr_types.tuples.tuple_portion_substitution
proveit.logic.booleans.conjunction.any_from_and
proveit.logic.booleans.conjunction.some_from_and
proveit.logic.equality.four_chain_transitivity
proveit.numbers.addition.add_complex_closure_bin
proveit.numbers.addition.add_int_closure_bin
proveit.numbers.addition.add_nat_closure_bin
proveit.numbers.addition.association
proveit.numbers.addition.commutation
proveit.numbers.addition.disassociation
proveit.numbers.addition.elim_zero_left
proveit.numbers.addition.elim_zero_right
proveit.numbers.addition.strong_bound_via_left_term_bound
proveit.numbers.addition.subtraction.add_cancel_triple_23
proveit.numbers.division.div_as_mult
proveit.numbers.division.div_complex_closure
proveit.numbers.division.frac_cancel_complete
proveit.numbers.division.frac_one_denom
proveit.numbers.division.mult_frac_cancel_denom_left
proveit.numbers.division.mult_frac_left
proveit.numbers.exponentiation.complex_x_to_first_power_is_x
proveit.numbers.exponentiation.neg_power_as_div
proveit.numbers.multiplication.association
proveit.numbers.multiplication.commutation
proveit.numbers.multiplication.disassociation
proveit.numbers.multiplication.distribute_through_sum
proveit.numbers.multiplication.elim_one_any
proveit.numbers.multiplication.elim_one_left
proveit.numbers.multiplication.elim_one_right
proveit.numbers.multiplication.mult_complex_closure_bin
proveit.numbers.negation.complex_closure
proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
proveit.numbers.number_sets.complex_numbers.real_within_complex
proveit.numbers.number_sets.complex_numbers.zero_is_complex
proveit.numbers.number_sets.integers.int_interval_within_int
proveit.numbers.number_sets.integers.nat_pos_within_int
proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
proveit.numbers.number_sets.integers.nat_within_int
proveit.numbers.number_sets.natural_numbers.fold_forall_natural_pos
proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
proveit.numbers.number_sets.rational_numbers.int_within_rational
proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
proveit.numbers.number_sets.real_numbers.nat_pos_within_real
proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
proveit.numbers.number_sets.real_numbers.rational_within_real
proveit.numbers.number_sets.real_numbers.zero_is_real
proveit.numbers.numerals.decimals.add_1_1
proveit.numbers.numerals.decimals.less_0_1
proveit.numbers.numerals.decimals.posnat1
proveit.numbers.numerals.decimals.posnat2
proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
proveit.numbers.ordering.less_is_not_eq_nat
proveit.numbers.summation.summation_complex_closure

Axioms required (directly or indirectly) to prove sum_first_n_int

proveit.core_expr_types.lambda_maps.lambda_substitution
proveit.core_expr_types.operations.operands_substitution
proveit.core_expr_types.tuples.empty_range_def
proveit.core_expr_types.tuples.range_extension_def
proveit.core_expr_types.tuples.tuple_eq_def
proveit.logic.booleans.bools_def
proveit.logic.booleans.conjunction.and_t_t
proveit.logic.booleans.disjunction.left_in_bool
proveit.logic.booleans.disjunction.or_f_f
proveit.logic.booleans.disjunction.or_t_f
proveit.logic.booleans.disjunction.right_in_bool
proveit.logic.booleans.eq_true_elim
proveit.logic.booleans.eq_true_intro
proveit.logic.booleans.false_not_true
proveit.logic.booleans.implication.affirmation_via_contradiction
proveit.logic.booleans.implication.denial_via_contradiction
proveit.logic.booleans.negation.negation_elim
proveit.logic.booleans.negation.not_f
proveit.logic.booleans.negation.not_t
proveit.logic.booleans.true_axiom
proveit.logic.equality.equality_in_bool
proveit.logic.equality.equals_reflexivity
proveit.logic.equality.equals_symmetry
proveit.logic.equality.equals_transitivity
proveit.logic.equality.not_equals_def
proveit.logic.equality.substitution
proveit.logic.sets.enumeration.enum_set_def
proveit.logic.sets.inclusion.proper_subset_def
proveit.logic.sets.inclusion.subset_eq_def
proveit.numbers.number_sets.natural_numbers.successor_in_nats
proveit.numbers.number_sets.natural_numbers.zero_in_nats
proveit.numbers.numerals.decimals.one_def
proveit.numbers.ordering.less_eq_def
proveit.numbers.ordering.transitivity_less_less
proveit.numbers.summation.sum_single
proveit.numbers.summation.sum_split_last

No theorems/conjectures depend upon sum_first_n_int