Nuprl Lemma : possible-majority_wf
∀T:Type. ∀eq:EqDecider(T). ∀L:T List. ∀x:T. (possible-majority(T;eq;L;x) ∈ ℙ)
Proof
Definitions occuring in Statement :
possible-majority: possible-majority(T;eq;L;x),
list: T List,
deq: EqDecider(T),
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
possible-majority: possible-majority(T;eq;L;x),
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
deq: EqDecider(T),
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
all_wf,
less_than_wf,
length_wf,
count_wf,
nat_wf,
equal_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
hypothesis,
multiplyEquality,
natural_numberEquality,
applyEquality,
setElimination,
rename,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}eq:EqDecider(T). \mforall{}L:T List. \mforall{}x:T. (possible-majority(T;eq;L;x) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_22_12
Last ObjectModification:
2015_12_26-PM-06_20_55
Theory : decidable!equality
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