### 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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