Nuprl Lemma : tcWO-induction-ext
∀[T:Type]. ∀[>:T ⟶ T ⟶ ℙ]. ∀[Q:T ⟶ ℙ]. TI(T;x,y.>[x;y];t.Q[t]) supposing tcWO(T;x,y.>[x;y])
Proof
Definitions occuring in Statement :
tcWO: tcWO(T;x,y.>[x; y]),
TI: TI(T;x,y.R[x; y];t.Q[t]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
subtract: n - m,
isr: isr(x),
bfalse: ff,
it: ⋅,
btrue: tt,
seq-normalize: seq-normalize(n;s),
bottom: ⊥,
ifthenelse: if b then t else f fi ,
tcWO-induction,
AF-induction2,
AF-induction,
basic_strong_bar_induction,
decidable__AFbar,
any: any x,
decidable__and2,
decidable__lt,
decidable__assert,
decidable__squash,
decidable__and,
decidable__less_than',
decidable_functionality,
squash_elim,
sq_stable_from_decidable,
iff_preserves_decidability,
sq_stable__from_stable,
stable__from_decidable,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
tcWO-induction,
lifting-strict-decide,
strict4-decide,
lifting-strict-less,
AF-induction2,
AF-induction,
basic_strong_bar_induction,
decidable__AFbar,
decidable__and2,
decidable__lt,
decidable__assert,
decidable__squash,
decidable__and,
decidable__less_than',
decidable_functionality,
squash_elim,
sq_stable_from_decidable,
iff_preserves_decidability,
sq_stable__from_stable,
stable__from_decidable
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[>:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q:T {}\mrightarrow{} \mBbbP{}]. TI(T;x,y.>[x;y];t.Q[t]) supposing tcWO(T;x,y.>[x;y])
Date html generated:
2018_05_21-PM-00_03_12
Last ObjectModification:
2018_05_19-AM-07_11_18
Theory : bar-induction
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