Nuprl Lemma : tagged-tag_wf2
∀[T,B:Type]. ∀[z:Atom]. ∀[x:T |+ z:B]. (x.tag ∈ Atom)
Proof
Definitions occuring in Statement :
tagged-tag: x.tag,
tagged+: T |+ z:B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tagged-tag: x.tag,
tagged+: T |+ z:B,
and: P ∧ Q,
cand: A c∧ B,
pi1: fst(t),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
or: P ∨ Q,
tag-case: z:T,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
isect2_decomp,
tag-case_wf,
spread_wf,
top_wf,
isect2_subtype_rel3,
subtype_rel_product,
ifthenelse_wf,
eq_atom_wf,
subtype_rel_wf,
tagged+_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation,
atomEquality,
because_Cache,
applyEquality,
productEquality,
independent_isectElimination,
inrFormation,
lambdaEquality,
instantiate,
universeEquality,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality
Latex:
\mforall{}[T,B:Type]. \mforall{}[z:Atom]. \mforall{}[x:T |+ z:B]. (x.tag \mmember{} Atom)
Date html generated:
2016_05_15-PM-06_47_22
Last ObjectModification:
2015_12_27-AM-11_48_02
Theory : general
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