Nuprl Lemma : run-lt-step-less
∀[M:Type ⟶ Type]. ∀[r:pRunType(P.M[P])].
∀[x,y:runEvents(r)]. run-event-step(x) < run-event-step(y) supposing x run-lt(r) y
supposing ∀e:runEvents(r). fst(fst(run-info(r;e))) < run-event-step(e)
Proof
Definitions occuring in Statement :
run-lt: run-lt(r),
run-event-step: run-event-step(e),
runEvents: runEvents(r),
run-info: run-info(r;e),
pRunType: pRunType(T.M[T]),
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,
uimplies: b supposing a,
run-lt: run-lt(r),
rel_plus: R+,
infix_ap: x f y,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
nat_plus: ℕ+,
or: P ∨ Q,
cand: A c∧ B,
decidable: Dec(P),
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
pi1: fst(t),
guard: {T},
subtract: n - m,
true: True
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[r:pRunType(P.M[P])].
\mforall{}[x,y:runEvents(r)]. run-event-step(x) < run-event-step(y) supposing x run-lt(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_50_19
Last ObjectModification:
2016_01_18-AM-00_12_48
Theory : process-model
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