Sentence examples for free proof from inspiring English sources

In street fashion, Mr. Cunningham, a photographer for The New York Times, has found something creative, life-affirming and free: proof of humanity amid the chaos of daily life.

For decidability, Moortgat (2009) gives a sequent presentation of LG in the format of a Display Calculus allowing cut-free proof search.

This leads to the desirable subformula property for GL, because all formulas that appear in a cut-free proof are subformulas of the endsequent formulas.

We shall provide a uniform and calculation-free proof of the existence of these elements using Steinberg's theorem ("Serre Conjecture I").

We give an interpolation-free proof of the known fact that a dyadic paraproduct is of Schatten von Neumann class Sp, if and only if its symbol is in the dyadic Besov space Bpd.

Figure 5 Bolzano's diagram-free proof of the IVT is an argument from what later became known as the Dedekind completeness of the real numbers: every non-empty set of reals bounded above (below) has a least upper bound (greatest lower bound).

For example, in the cut-free proof of Solution 2, the existentially quantified variable for the time when the object reaches height zero is instantiated by a ground term that denotes exactly when this happens.

This is advantageous in certain cases, for in a cut-free proof it is easy, via Gentzen's Midsequent Theorem [11] or more general Herbrand sequent extraction algorithms [16], to extract a Herbrand disjunction [12] that contains instances of the quantified variables of the problem.

Within linear logic, the focused proof system of Andreoli provides an elegant and comprehensive normal form for cut-free proofs.

An important normal form theorem for the structure of cut-free proofs was provided by Andreoli (1992).

is an example of a stratified theorem of first-order logic that has stratified proofs but no stratified cut-free proofs.