Nuprl Lemma : equal-nil-sq-nil

`∀[T:Type]. ∀[L:T List].  L ~ [] supposing L = [] ∈ (T List)`

Proof

Definitions occuring in Statement :  nil: `[]` list: `T List` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type` sqequal: `s ~ t` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` not: `¬A` implies: `P `` Q` false: `False` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  no-member-sq-nil null_nil_lemma btrue_wf member-implies-null-eq-bfalse and_wf equal_wf list_wf null_wf btrue_neq_bfalse l_member_wf nil_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination lambdaFormation sqequalRule hypothesis dependent_set_memberEquality independent_pairFormation equalityTransitivity equalitySymmetry applyEquality lambdaEquality setElimination rename productElimination setEquality independent_functionElimination voidElimination because_Cache sqequalAxiom isect_memberEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].    L  \msim{}  []  supposing  L  =  []

Date html generated: 2016_05_14-PM-02_50_08
Last ObjectModification: 2015_12_26-PM-02_36_31

Theory : list_1

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