Nuprl Lemma : assert-null-base
∀[as:Base]. uiff(null(as) ~ tt;as ~ [])
Proof
Definitions occuring in Statement :
null: null(as),
nil: [],
btrue: tt,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bool: 𝔹,
null: null(as),
has-value: (a)↓,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
nil: [],
it: ⋅,
btrue: tt,
or: P ∨ Q,
bfalse: ff,
not: ¬A,
false: False
Lemmas referenced :
not-btrue-sqeq-bfalse,
bottom_diverge,
has-value-implies-dec-ispair-2,
has-value-implies-dec-isaxiom-2,
base_wf,
btrue_wf,
unit_wf2,
union-value-type,
bool_wf,
value-type-has-value,
subtype_rel_self,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
sqequalRule,
callbyvalueIspair,
dependent_functionElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
productElimination,
independent_pairEquality,
isect_memberEquality,
unionElimination,
voidElimination
Latex:
\mforall{}[as:Base]. uiff(null(as) \msim{} tt;as \msim{} [])
Date html generated:
2016_05_14-AM-06_30_39
Last ObjectModification:
2016_01_14-PM-08_25_15
Theory : list_0
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