### Nuprl Lemma : ffor_wf

`∀T:Type. ∀Q:(T List) ⟶ Type. ∀b0:Q[[]]. ∀b1:∀x:T. Q[[x]]. ∀up:∀ys,ys':T List.  (Q[ys] `` Q[ys'] `` Q[ys @ ys']).`
`∀zs:T List.`
`  (ffor(b0;b1;up;zs) ∈ Q[zs])`

Proof

Definitions occuring in Statement :  ffor: `ffor(b0;b1;up;zs)` append: `as @ bs` cons: `[a / b]` nil: `[]` list: `T List` so_apply: `x[s]` all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` 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` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` guard: `{T}` or: `P ∨ Q` ffor: `ffor(b0;b1;up;zs)` ycomb: `Y` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` 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)` append: `as @ bs`
Lemmas referenced :  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 nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases list_ind_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 list_ind_cons_lemma list_wf cons_wf nil_wf all_wf append_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut thin introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry cumulativity applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate imageElimination functionExtensionality functionEquality universeEquality

Latex:
\mforall{}T:Type.  \mforall{}Q:(T  List)  {}\mrightarrow{}  Type.  \mforall{}b0:Q[[]].  \mforall{}b1:\mforall{}x:T.  Q[[x]].  \mforall{}up:\mforall{}ys,ys':T  List.
(Q[ys]  {}\mRightarrow{}  Q[ys']  {}\mRightarrow{}  Q[ys  @  ys']).
\mforall{}zs:T  List.
(ffor(b0;b1;up;zs)  \mmember{}  Q[zs])

Date html generated: 2017_10_01-AM-10_00_33
Last ObjectModification: 2017_03_03-PM-01_02_17

Theory : mset

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