Nuprl Lemma : sq_stable__vdf-eq
∀[A,B:Type]. ∀[C:A ⟶ B ⟶ Type]. ∀[f:very-dep-fun(A;B;a,b.C[a;b])]. ∀[L:(a:A × b:B × C[a;b]) List].
SqStable(vdf-eq(A;f;L))
Proof
Definitions occuring in Statement :
very-dep-fun: very-dep-fun(A;B;a,b.C[a; b]),
vdf-eq: vdf-eq(A;f;L),
list: T List,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
vdf-eq-witness,
squash_wf,
vdf-eq_wf,
list_wf,
very-dep-fun_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
sqequalHypSubstitution,
imageElimination,
introduction,
cut,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
applyEquality,
universeIsType,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
productEquality,
functionIsType,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[C:A {}\mrightarrow{} B {}\mrightarrow{} Type]. \mforall{}[f:very-dep-fun(A;B;a,b.C[a;b])]. \mforall{}[L:(a:A \mtimes{} b:B \mtimes{} C[a;b]) List].
SqStable(vdf-eq(A;f;L))
Date html generated:
2020_05_19-PM-09_40_46
Last ObjectModification:
2020_03_06-PM-01_24_30
Theory : co-recursion-2
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