Nuprl Lemma : tagged-val_wf
∀[T:Atom ⟶ Type]. ∀[x:tagged(x.T[x])]. (x.val ∈ T[x.tag])
Proof
Definitions occuring in Statement :
tagged-val: x.val,
tagged-tag: x.tag,
tagged: tagged(x.T[x]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tagged-val: x.val,
tagged: tagged(x.T[x]),
pi2: snd(t),
tagged-tag: x.tag,
pi1: fst(t),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
tagged_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
lambdaEquality,
applyEquality,
atomEquality,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Atom {}\mrightarrow{} Type]. \mforall{}[x:tagged(x.T[x])]. (x.val \mmember{} T[x.tag])
Date html generated:
2016_05_15-PM-06_47_47
Last ObjectModification:
2015_12_27-AM-11_47_33
Theory : general
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