### Nuprl Lemma : append-finite-nat-seq-assoc

`∀[f,g,h:finite-nat-seq()].  (f**g**h = f**g**h ∈ finite-nat-seq())`

Proof

Definitions occuring in Statement :  append-finite-nat-seq: `f**g` finite-nat-seq: `finite-nat-seq()` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` finite-nat-seq: `finite-nat-seq()` append-finite-nat-seq: `f**g` mk-finite-nat-seq: `f^(n)` nat: `ℕ` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` and: `P ∧ Q` int_seg: `{i..j-}` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` less_than: `a < b` less_than': `less_than'(a;b)` true: `True` squash: `↓T` lelt: `i ≤ j < k` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` le: `A ≤ B` subtype_rel: `A ⊆r B` subtract: `n - m`
Lemmas referenced :  nat_properties decidable__equal_int satisfiable-full-omega-tt intformnot_wf intformeq_wf itermAdd_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf decidable__le intformand_wf intformle_wf itermConstant_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma le_wf int_seg_wf nat_wf finite-nat-seq_wf lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int top_wf less_than_wf lelt_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot subtract_wf int_seg_properties itermSubtract_wf int_term_value_subtract_lemma intformless_wf int_formula_prop_less_lemma minus-add minus-one-mul add-swap add-commutes add-associates decidable__lt
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution productElimination thin sqequalRule dependent_pairEquality extract_by_obid isectElimination hypothesisEquality hypothesis setElimination rename dependent_functionElimination addEquality unionElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll dependent_set_memberEquality because_Cache independent_pairFormation functionEquality axiomEquality functionExtensionality lambdaFormation equalityElimination equalityTransitivity equalitySymmetry lessCases sqequalAxiom imageMemberEquality baseClosed imageElimination independent_functionElimination applyEquality promote_hyp instantiate cumulativity

Latex:
\mforall{}[f,g,h:finite-nat-seq()].    (f**g**h  =  f**g**h)

Date html generated: 2017_04_20-AM-07_29_49
Last ObjectModification: 2017_02_27-PM-06_01_03

Theory : continuity

Home Index