Nuprl Lemma : strict-majority-or-first_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:{L:T List| ||L|| ≥ 1 } ]. (strict-majority-or-first(eq;L) ∈ T)
Proof
Definitions occuring in Statement :
strict-majority-or-first: strict-majority-or-first(eq;L),
length: ||as||,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strict-majority-or-first: strict-majority-or-first(eq;L),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
ge: i ≥ j ,
so_apply: x[s]
Lemmas referenced :
strict-majority_wf,
unit_wf2,
hd_wf,
equal_wf,
set_wf,
list_wf,
ge_wf,
length_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
unionEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
unionElimination,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
lambdaEquality,
natural_numberEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:\{L:T List| ||L|| \mgeq{} 1 \} ]. (strict-majority-or-first(eq;L) \mmember{} T)
Date html generated:
2019_06_20-PM-01_54_57
Last ObjectModification:
2018_08_21-PM-01_55_23
Theory : decidable!equality
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