### Nuprl Lemma : map-tuple-ap2-tuple

`∀[n:ℕ]. ∀[f,x:Top]. ∀[g,t:n-tuple(n)].`
`  (map-tuple(n;f;ap2-tuple(n;g;x;t)) ~ ap2-tuple(n;map-tuple(n;λh,x,z. (f (h x z));g);x;t))`

Proof

Definitions occuring in Statement :  map-tuple: `map-tuple(len;f;t)` ap2-tuple: `ap2-tuple(len;f;x;t)` n-tuple: `n-tuple(n)` nat: `ℕ` uall: `∀[x:A]. B[x]` top: `Top` apply: `f a` lambda: `λx.A[x]` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` top: `Top` tuple: `tuple(n;i.F[i])` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` guard: `{T}` or: `P ∨ Q` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` decidable: `Dec(P)` nil: `[]` it: `⋅` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)`
Lemmas referenced :  n-tuple_wf top_wf nat_wf ap2-tuple_wf_ntuple map-tuple_wf_ntuple upto_wf list_wf int_seg_wf nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf equal-wf-T-base colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases map_nil_lemma product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int map_cons_lemma map-tuple-as-tuple ap2-tuple-as-tuple select-tuple-tuple
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis sqequalAxiom extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule isect_memberEquality because_Cache voidElimination voidEquality setElimination rename natural_numberEquality lambdaFormation intWeakElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination independent_pairFormation computeAll independent_functionElimination applyEquality unionElimination promote_hyp hypothesis_subsumption productElimination equalityTransitivity equalitySymmetry applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate cumulativity imageElimination

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f,x:Top].  \mforall{}[g,t:n-tuple(n)].
(map-tuple(n;f;ap2-tuple(n;g;x;t))  \msim{}  ap2-tuple(n;map-tuple(n;\mlambda{}h,x,z.  (f  (h  x  z));g);x;t))

Date html generated: 2017_04_17-AM-09_29_50
Last ObjectModification: 2017_02_27-PM-05_30_24

Theory : tuples

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