Nuprl Lemma : Wleq_weakening2
∀[A:Type]. ∀[B:A ⟶ Type]. ∀w1,w2:W(A;a.B[a]). w1 ≤ w2 supposing w1 = w2 ∈ W(A;a.B[a])
Proof
Definitions occuring in Statement :
Wcmp: Wcmp(A;a.B[a];leq),
W: W(A;a.B[a]),
btrue: tt,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
infix_ap: x f y,
implies: P ⇒ Q,
prop: ℙ,
Wcmp: Wcmp(A;a.B[a];leq),
Wsup: Wsup(a;b),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
exists: ∃x:A. B[x],
guard: {T}
Lemmas referenced :
W-induction,
Wcmp_wf,
btrue_wf,
W_wf,
all_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
equalitySymmetry,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
functionExtensionality,
cumulativity,
independent_functionElimination,
functionEquality,
because_Cache,
dependent_functionElimination,
hyp_replacement,
Error :applyLambdaEquality,
universeEquality,
dependent_pairFormation
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}w1,w2:W(A;a.B[a]). w1 \mleq{} w2 supposing w1 = w2
Date html generated:
2016_10_21-AM-09_46_32
Last ObjectModification:
2016_07_12-AM-05_06_06
Theory : co-recursion
Home
Index