Nuprl Lemma : bar-equal-equiv
∀[T:Type]. EquivRel(bar-base(T);x,y.bar-equal(T;x;y))
Proof
Definitions occuring in Statement :
bar-equal: bar-equal(T;x;y),
bar-base: bar-base(T),
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
bar-equal: bar-equal(T;x;y),
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
so_lambda: λ2x.t[x],
so_apply: x[s],
trans: Trans(T;x,y.E[x; y]),
guard: {T}
Lemmas referenced :
bar-converges_wf,
bar-base_wf,
all_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
lambdaEquality,
universeEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. EquivRel(bar-base(T);x,y.bar-equal(T;x;y))
Date html generated:
2016_05_14-AM-06_20_31
Last ObjectModification:
2015_12_26-PM-00_00_39
Theory : co-recursion
Home
Index