Nuprl Lemma : istype-mrecind

[L:MutualRectypeSpec]. ∀[P:mobj(L) ⟶ TYPE].  istype(mrecind(L;x.P[x]))


Proof




Definitions occuring in Statement :  mrecind: mrecind(L;x.P[x]) mobj: mobj(L) mrec_spec: MutualRectypeSpec istype: istype(T) uall: [x:A]. B[x] so_apply: x[s] function: x:A ⟶ B[x]
Definitions unfolded in proof :  uall: [x:A]. B[x] mrecind: mrecind(L;x.P[x]) all: x:A. B[x] member: t ∈ T mkinds: mKinds prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl) implies:  Q so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] int_seg: {i..j-} uimplies: supposing a lelt: i ≤ j < k and: P ∧ Q le: A ≤ B less_than: a < b squash: T decidable: Dec(P) or: P ∨ Q not: ¬A satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False top: Top prop: subtype_rel: A ⊆B less_than': less_than'(a;b) mrec: mrec(L;i) uiff: uiff(P;Q) outl: outl(x) isl: isl(x) assert: b ifthenelse: if then else fi  btrue: tt true: True guard: {T} iff: ⇐⇒ Q rev_implies:  Q prec: prec(lbl,p.a[lbl; p];i) so_apply: x[s] ext-eq: A ≡ B cand: c∧ B outr: outr(x) bnot: ¬bb bfalse: ff list: List l_all: (∀x∈L.P[x])
Lemmas referenced :  mkinds_wf istype-less_than length_wf mrec-spec_wf tuple-type_wf map_wf prec_wf list_wf istype-universe mobj_wf mrec_spec_wf int_seg_wf select_wf int_seg_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf istype-int int_formula_prop_and_lemma istype-void int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf decidable__lt intformless_wf int_formula_prop_less_lemma select-tuple_wf int_seg_subtype_nat istype-false select-map subtype_rel_list top_wf equal_wf squash_wf true_wf inl-one-one outl_wf assert_wf btrue_wf bfalse_wf mrec_wf btrue_neq_bfalse not-0-eq-1 inr-one-one subtype_rel_self iff_weakening_equal mobj-ext map-length outr_wf bnot_wf istype-true mk-prec_wf prec-arg-types_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  sqequalRule Error :functionIsType,  Error :universeIsType,  cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename Error :setIsType,  Error :inhabitedIsType,  natural_numberEquality instantiate unionEquality cumulativity atomEquality universeEquality Error :lambdaFormation_alt,  Error :lambdaEquality_alt,  equalityTransitivity equalitySymmetry unionElimination Error :equalityIstype,  dependent_functionElimination independent_functionElimination Error :unionIsType,  applyLambdaEquality because_Cache Error :TYPEIsType,  closedConclusion independent_isectElimination productElimination imageElimination approximateComputation Error :dependent_pairFormation_alt,  int_eqEquality Error :isect_memberEquality_alt,  voidElimination independent_pairFormation applyEquality Error :dependent_set_memberEquality_alt,  Error :productIsType,  promote_hyp hyp_replacement Error :inlEquality_alt,  imageMemberEquality baseClosed Error :TYPEMemberIsType,  Error :dependent_pairEquality_alt,  Error :inrEquality_alt

Latex:
\mforall{}[L:MutualRectypeSpec].  \mforall{}[P:mobj(L)  {}\mrightarrow{}  TYPE].    istype(mrecind(L;x.P[x]))



Date html generated: 2019_06_20-PM-02_16_02
Last ObjectModification: 2019_03_12-PM-11_10_11

Theory : tuples


Home Index