Nuprl Lemma : well-founded-run-pred
∀[M:Type ⟶ Type]
∀r:pRunType(P.M[P])
SWellFounded(x run-pred(r) y) supposing ∀e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
Proof
Definitions occuring in Statement :
run-pred: run-pred(r),
run-event-step: run-event-step(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRunType: pRunType(T.M[T]),
strongwellfounded: SWellFounded(R[x; y]),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
pi1: fst(t),
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
pi1: fst(t),
subtype_rel: A ⊆r B,
nat: ℕ,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
prop: ℙ,
infix_ap: x f y,
guard: {T}
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
\mforall{}r:pRunType(P.M[P])
SWellFounded(x run-pred(r) y)
supposing \mforall{}e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
Date html generated:
2016_05_17-AM-10_49_07
Last ObjectModification:
2015_12_29-PM-05_21_35
Theory : process-model
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