% Leo-III cross-check.
% PR-011, our definition: MP-008, MP-010, the definition and OP-007 give that the universe is caused.
% Vocabulary.  Nothing is assumed about these symbols.
thf(ex_type, type, ex: $i > $o).                     % (ex @ X): X exists
thf(ess_type, type, ess: $i > $o).                   % (ess @ X): X's existence is from its nature
thf(gives_type, type, gives: $i > $i > $o).          % (gives @ Y @ X): Y gives existence to X
thf(nec_type, type, nec: $i > $o).
thf(poss_type, type, poss: $i > $o).
thf(ta_type, type, through_another: $i > $o).
thf(nec_def, definition, nec = (^[X:$i]: ((ex @ X) & (ess @ X)))).            % necessary in itself
thf(poss_def, definition, poss = (^[X:$i]: ((ex @ X) & ~ (ess @ X)))).        % possible in itself
thf(ta_def, definition, through_another = (^[X:$i]: ?[Y:$i]: (gives @ Y @ X))). % something gives X existence
thf(part_type, type, part: $i > $i > $o).
thf(u_type, type, u: $i).
thf(mp008, axiom, ![X:$i]: (((ex @ X) & ~ (through_another @ X)) => (ess @ X))).   % MP-008
thf(mp010, axiom, ![A:$i]: (((?[P:$i]: (part @ P @ A)) & (![P:$i]: ((part @ P @ A) => ~ (ess @ P)))) => ~ (ess @ A))).  % MP-010
thf(narrow, axiom, ![P:$i]: ((part @ P @ u) => ~ (ess @ P))).                           % our definition of the universe
thf(op007, axiom, (ex @ u) & (?[P:$i]: (part @ P @ u))).                                % OP-007
thf(conclusion, conjecture, through_another @ u).