Nuprl Lemma : cons_wf
∀[S:Type]. ∀[a:S]. ∀[b:S List]. ([a / b] ∈ S List)
Proof
Definitions occuring in Statement :
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cons: [a / b],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
list-ext,
subtype_rel_b-union-right,
unit_wf2,
list_wf,
ext-eq_inversion,
b-union_wf,
subtype_rel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_pairEquality,
hypothesis,
applyEquality,
productEquality,
hypothesisEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[S:Type]. \mforall{}[a:S]. \mforall{}[b:S List]. ([a / b] \mmember{} S List)
Date html generated:
2016_05_14-AM-06_25_50
Last ObjectModification:
2015_12_26-PM-00_42_23
Theory : list_0
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