Nuprl Lemma : is-list-if-has-value-rec-subtype-unit
∀[t:Base]. (is-list-if-has-value-rec(t) ⊆r Unit)
Proof
Definitions occuring in Statement :
is-list-if-has-value-rec: is-list-if-has-value-rec(t),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
unit: Unit,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
is-list-if-has-value-rec: is-list-if-has-value-rec(t),
is-list-if-has-value-fun: is-list-if-has-value-fun(t;n),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
unit: Unit
Lemmas referenced :
false_wf,
le_wf,
primrec0_lemma,
is-list-if-has-value-rec_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
lemma_by_obid,
thin,
hypothesisEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality
Latex:
\mforall{}[t:Base]. (is-list-if-has-value-rec(t) \msubseteq{}r Unit)
Date html generated:
2016_05_15-PM-10_08_41
Last ObjectModification:
2015_12_27-PM-06_00_04
Theory : eval!all
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