Nuprl Lemma : ts-reachable-induction2
∀ts:transition-system{i:l}
∀[P:ts-reachable(ts) ⟶ ℙ]
(P[ts-init(ts)]
⇒ (∀x,y:ts-reachable(ts). (P[x] ⇒ (x ts-rel(ts) y) ⇒ P[y]))
⇒ {∀x:ts-type(ts). ((ts-init(ts) (ts-rel(ts)^*) x) ⇒ P[x])})
Proof
Definitions occuring in Statement :
ts-reachable: ts-reachable(ts),
ts-rel: ts-rel(ts),
ts-init: ts-init(ts),
ts-type: ts-type(ts),
transition-system: transition-system{i:l},
rel_star: R^*,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
infix_ap: x f y,
ts-reachable: ts-reachable(ts),
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
ts-reachable-induction3,
ts-rel_wf,
rel_star_wf,
ts-type_wf,
ts-init_wf,
ts-reachable_wf,
subtype_rel_wf,
all_wf,
infix_ap_wf,
subtype_rel_set,
subtype_rel_dep_function,
ts-init_wf_reachable,
transition-system_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberFormation,
isectElimination,
independent_functionElimination,
applyEquality,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
sqequalRule,
lambdaEquality,
setEquality,
universeEquality,
cumulativity,
functionEquality,
instantiate,
independent_isectElimination
Latex:
\mforall{}ts:transition-system\{i:l\}
\mforall{}[P:ts-reachable(ts) {}\mrightarrow{} \mBbbP{}]
(P[ts-init(ts)]
{}\mRightarrow{} (\mforall{}x,y:ts-reachable(ts). (P[x] {}\mRightarrow{} (x ts-rel(ts) y) {}\mRightarrow{} P[y]))
{}\mRightarrow{} \{\mforall{}x:ts-type(ts). ((ts-init(ts) rel\_star(ts-type(ts); ts-rel(ts)) x) {}\mRightarrow{} P[x])\})
Date html generated:
2016_05_15-PM-05_42_04
Last ObjectModification:
2015_12_27-PM-00_31_39
Theory : general
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