Sentence examples for closed instances from inspiring English sources

Ad 3: Open proofs are justified by considering their closed instances.

These closed instances are obtained by replacing their open assumptions with closed proofs of them, and their open variables with closed terms.

For that, it suffices to show that, given any finite set of closed instances of axioms, one can assign numerical values to terms in such a way that all the axioms are true under the interpretation.

By pushing all substitutions to the axioms and replacing free variables by the constant 0, it suffices to show that there is no propositional proof of 0 = 1 from a finite set of closed instances of the axioms.

Before the shutdown, Mr. Daugaard had offered to spend state money to keep Mount Rushmore open on a limited basis — the gift shop would have remained closed, for instance — and staff the park with state workers.

However, there exist many closed areas (for instance, enclosed bays) which present a serious quality problem caused by domestic/industrial contaminants, due to the insufficient seawater exchange.

If Prim(A) has a dense Gδ consisting of closed points (for instance, if Prim(A) is a T1-space) and A is unital, then Mloc(A) is its own local multiplier algebra and has only inner derivations.

Cases will be referred to the Clinic from a number of government institutions, including, for example, the Ministry of Education, the Ombudsman's Office, the State Committee for Family, Women, Children's Affairs, the commission on Minors, Police and Courts, and also from closed institutions, for instance, children who have been released from the Special School.

Within modern actinopterygians, the distribution of an open BHC does not seem to carry a strong phylogenetic signal, as the canal can be either open or closed in closely related species (for instance within the Galaxioidea [ 61]).

Tarski only explicitly considered closed sets also closed under substitution instances for some consequence relations; he never considered (at least explicitly) the substitution invariance condition for consequence relations.

From a grammatical point of view, the Committee took care to leave open questions open, although in some instances a closed question would have sounded better to Italian ears.