Nuprl Lemma : dlo-eq_wf

dlo-eq() ∈ dl-Obj() ⟶ dl-Obj() ⟶ 𝔹


Proof



Definitions occuring in Statement :  dlo-eq: dlo-eq(),  dl-Obj: dl-Obj(),  bool: 𝔹,  member: t ∈ T,  function: x:A ⟶ B[x]
Definitions unfolded in proof :  dlo-eq: dlo-eq(),  member: t ∈ T,  subtype_rel: A ⊆r B,  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  or: P ∨ Q,  uimplies: b supposing a,  sq_type: SQType(T),  implies: P ⇒ Q,  guard: {T},  uiff: uiff(P;Q),  and: P ∧ Q,  nat: ℕ,  bfalse: ff,  band: p ∧b q,  ifthenelse: if b then t else f fi ,  so_lambda: λ2x.t[x],  so_apply: x[s],  so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),  so_apply: x[s1;s2;s3;s4],  so_lambda: λ2x y.t[x; y],  so_apply: x[s1;s2]
Lemmas referenced :  dl-Obj_wf,  bool_wf,  subtype-TYPE,  eq_atom_wf,  dl-kind_wf,  bool_cases,  subtype_base_sq,  bool_subtype_base,  eqtt_to_assert,  band_wf,  btrue_wf,  assert_of_eq_atom,  dl-aprog?_wf,  dl-obj-prog_wf,  eq_int_wf,  dl-aprog-1_wf,  bfalse_wf,  istype-nat,  dl-comp?_wf,  dl-prog-obj_wf,  dl-comp-1_wf,  dl-comp-2_wf,  dl-prog_wf,  dl-choose?_wf,  dl-choose-1_wf,  dl-choose-2_wf,  dl-iterate?_wf,  dl-iterate-1_wf,  dl-test?_wf,  dl-prop-obj_wf,  dl-test-1_wf,  dl-prop_wf,  dl-aprop?_wf,  dl-obj-prop_wf,  dl-aprop-1_wf,  dl-false?_wf,  dl-implies?_wf,  dl-implies-1_wf,  dl-implies-2_wf,  dl-and?_wf,  dl-and-1_wf,  dl-and-2_wf,  dl-or?_wf,  dl-or-1_wf,  dl-or-2_wf,  dl-box?_wf,  dl-box-1_wf,  dl-box-2_wf,  dl-diamond?_wf,  dl-diamond-1_wf,  dl-diamond-2_wf,  dl-ind_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  lambdaEquality_alt,  cut,  functionEquality,  introduction,  extract_by_obid,  hypothesis,  applyEquality,  thin,  sqequalHypSubstitution,  sqequalRule,  universeIsType,  isectElimination,  hypothesisEquality,  because_Cache,  tokenEquality,  dependent_functionElimination,  unionElimination,  instantiate,  cumulativity,  independent_isectElimination,  equalityTransitivity,  equalitySymmetry,  independent_functionElimination,  productElimination,  setElimination,  rename,  inhabitedIsType,  functionIsType
Latex:
dlo-eq()  \mmember{}  dl-Obj()  {}\mrightarrow{}  dl-Obj()  {}\mrightarrow{}  \mBbbB{}


Date html generated: 2019_10_15-AM-11_42_43
Last ObjectModification: 2019_04_04-PM-06_34_58

Theory : dynamic!logic


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