Nuprl Lemma : has-value-implies-dec-isaxiom-2
∀t:Base. ((t)↓ ⇒ ((t ~ Ax) ∨ (∀a,b:Base. (if t = Ax then a otherwise b ~ b))))
Proof
Definitions occuring in Statement :
has-value: (a)↓,
isaxiom: if z = Ax then a otherwise b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
base: Base,
sqequal: s ~ t,
axiom: Ax
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
uimplies: b supposing a,
has-value: (a)↓,
false: False,
top: Top,
sq_type: SQType(T)
Lemmas referenced :
top_wf,
not_zero_sqequal_one,
is-exception_wf,
has-value_wf_base,
subtype_rel_self,
subtype_base_sq,
base_wf,
all_wf,
has-value-implies-dec-isaxiom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
baseClosed,
independent_functionElimination,
hypothesis,
unionElimination,
inlFormation,
isectElimination,
sqequalRule,
lambdaEquality,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
inrFormation,
instantiate,
because_Cache,
independent_isectElimination,
isaxiomCases,
divergentSqle,
voidElimination,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality,
voidEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}t:Base. ((t)\mdownarrow{} {}\mRightarrow{} ((t \msim{} Ax) \mvee{} (\mforall{}a,b:Base. (if t = Ax then a otherwise b \msim{} b))))
Date html generated:
2016_05_13-PM-03_22_38
Last ObjectModification:
2016_01_14-PM-06_46_54
Theory : call!by!value_1
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