A semantics is defined by induction on the type system rules, for which coherence is trivial.
For any e ∈ E f, C ( e ) is defined by induction.
The preimage (x({vec {i}}, w')) of (z({vec {i}}, w)) for every ({vec {i}}) and w is defined by induction on the length of w and the sum of ({vec {i}}_j) (the base of induction, where ({vec {i}}={vec {1}}) is obvious).
That is, if the assumptions in Theorem 2.8 hold, then u is a constant on the set (overline{bigcup _{n=0}^infty varLambda _n}), where (varLambda _n)'s are defined by induction, begin{aligned} varLambda _0 = {x^0}, varLambda _{n+1}= bigcup _{xin Dcap varLambda _n}[text { supp},nu (x,cdot )+x].
Namely, if (u(x^0,t^0)=M) with (x^0in D) and (t^0in (0,then then (uequiv M) on the set (overline{bigcup _{n=0}^infty varLambda _n}), where ({tilde{varLambda }}_n)'s are defined by induction, begin{aligned} {tilde{varLambda }}_0 = {x^0}, {tilde{varLambda }}_{n+1}= bigcup _{xin D{cap {tilde{varLambda }}}_n}[text { supp},nu (t^0,x,cdot )+x].
Don't be defined by a label.
Fruit ripening initiation was defined by the induction of ethylene starting from red ripe (0.65 μlKg-1h-1) and increasing at T1Ctrl (120 DAFB) and T2Ctrl (123 DAFB), producing 16.11 μlKg-1h-1 μlKg-1h-1 μlKg-1h-1 of ethylene respectively.
In the ID-logic axiomatization of the situation calculus, fluents and causality predicates are defined by simultaneous induction on the well-founded poset of situations.
Responders were defined by the induction of anti-Tat Ab.
A generalized linear model was applied based on a negative binomial distribution and an overall test was conducted to determine which genes varied in expression among any of the seven treatment groups, where a treatment group was defined by a strain-by-induction condition combination (see Methods for details).
