Nuprl Lemma : coW-equiv-equiv_rel
∀[A:𝕌']. ∀B:A ⟶ Type. EquivRel(coW(A;a.B[a]);w,w'.coW-equiv(a.B[a];w;w'))
Proof
Definitions occuring in Statement :
coW-equiv: coW-equiv(a.B[a];w;w'),
coW: coW(A;a.B[a]),
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
guard: {T},
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
uimplies: b supposing a
Lemmas referenced :
coW_wf,
coW-equiv_inversion,
coW-equiv_wf,
coW-equiv_transitivity,
coW-equiv_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
applyEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}B:A {}\mrightarrow{} Type. EquivRel(coW(A;a.B[a]);w,w'.coW-equiv(a.B[a];w;w'))
Date html generated:
2018_07_25-PM-01_48_01
Last ObjectModification:
2018_07_11-AM-11_47_44
Theory : co-recursion
Home
Index