### Nuprl Lemma : seq-cons_wf

`∀[T:Type]. ∀[a:T]. ∀[s:sequence(T)].  (seq-cons(a;s) ∈ sequence(T))`

Proof

Definitions occuring in Statement :  seq-cons: `seq-cons(a;s)` sequence: `sequence(T)` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` seq-cons: `seq-cons(a;s)` sequence: `sequence(T)` nat: `ℕ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` rev_implies: `P `` Q` implies: `P `` Q` false: `False` prop: `ℙ` uiff: `uiff(P;Q)` uimplies: `b supposing a` sq_stable: `SqStable(P)` squash: `↓T` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` int_seg: `{i..j-}` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` lelt: `i ≤ j < k`
Lemmas referenced :  decidable__le false_wf not-le-2 sq_stable__le condition-implies-le minus-add minus-one-mul zero-add minus-one-mul-top add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel le_wf eq_int_wf bool_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base iff_transitivity assert_wf bnot_wf not_wf equal-wf-T-base iff_weakening_uiff assert_of_bnot assert_of_eq_int int_seg_wf subtract_wf not-equal-2 minus-zero minus-minus decidable__lt not-lt-2 less-iff-le and_wf less_than_wf sequence_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution productElimination thin dependent_pairEquality dependent_set_memberEquality addEquality setElimination rename because_Cache hypothesis natural_numberEquality extract_by_obid dependent_functionElimination hypothesisEquality unionElimination independent_pairFormation lambdaFormation voidElimination independent_functionElimination independent_isectElimination isectElimination imageMemberEquality baseClosed imageElimination applyEquality lambdaEquality isect_memberEquality voidEquality intEquality minusEquality equalityElimination equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp instantiate cumulativity impliesFunctionality functionExtensionality functionEquality axiomEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[a:T].  \mforall{}[s:sequence(T)].    (seq-cons(a;s)  \mmember{}  sequence(T))

Date html generated: 2018_07_25-PM-01_28_57
Last ObjectModification: 2018_06_12-PM-10_26_52

Theory : arithmetic

Home Index