Nuprl Lemma : IdNotHomotopicConst_wf

∀[n:ℕ]. (IdNotHomotopicConst(n) ∈ ℙ)


Proof




Definitions occuring in Statement :  IdNotHomotopicConst: IdNotHomotopicConst(n),  nat: ℕ,  uall: ∀[x:A]. B[x],  prop: ℙ,  member: t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  IdNotHomotopicConst: IdNotHomotopicConst(n),  all: ∀x:A. B[x],  top: Top,  and: P ∧ Q,  prop: ℙ,  so_lambda: λ2x.t[x],  nat: ℕ,  ge: i ≥ j ,  decidable: Dec(P),  or: P ∨ Q,  uimplies: b supposing a,  not: ¬A,  implies: P ⇒ Q,  satisfiable_int_formula: satisfiable_int_formula(fmla),  exists: ∃x:A. B[x],  false: False,  cand: A c∧ B,  iff: P ⇐⇒ Q,  rev_implies: P ⇐ Q,  le: A ≤ B,  less_than': less_than'(a;b),  subtype_rel: A ⊆r B,  real-unit-sphere: S(n),  so_apply: x[s]
Lemmas referenced :  member_rccint_lemma,  istype-void,  not_wf,  exists_wf,  real_wf,  rleq_wf,  int-to-real_wf,  real-unit-sphere_wf,  all_wf,  req-vec_wf,  nat_properties,  decidable__le,  full-omega-unsat,  intformand_wf,  intformnot_wf,  intformle_wf,  itermConstant_wf,  itermAdd_wf,  itermVar_wf,  istype-int,  int_formula_prop_and_lemma,  int_formula_prop_not_lemma,  int_formula_prop_le_lemma,  int_term_value_constant_lemma,  int_term_value_add_lemma,  int_term_value_var_lemma,  int_formula_prop_wf,  istype-le,  rleq-int,  istype-false,  rleq_weakening_equal,  req_wf,  istype-nat
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isect_memberFormation_alt,  introduction,  cut,  sqequalRule,  extract_by_obid,  sqequalHypSubstitution,  dependent_functionElimination,  thin,  isect_memberEquality_alt,  voidElimination,  hypothesis,  isectElimination,  functionEquality,  closedConclusion,  setEquality,  productEquality,  natural_numberEquality,  hypothesisEquality,  lambdaFormation_alt,  universeIsType,  setElimination,  rename,  because_Cache,  lambdaEquality_alt,  dependent_set_memberEquality_alt,  addEquality,  unionElimination,  independent_isectElimination,  approximateComputation,  independent_functionElimination,  dependent_pairFormation_alt,  int_eqEquality,  independent_pairFormation,  applyEquality,  productElimination,  productIsType,  inhabitedIsType,  equalityTransitivity,  equalitySymmetry,  setIsType,  functionIsType,  axiomEquality

Latex:
\mforall{}[n:\mBbbN{}].  (IdNotHomotopicConst(n)  \mmember{}  \mBbbP{})



Date html generated: 2019_10_30-AM-11_29_57
Last ObjectModification: 2019_08_05-PM-04_05_26

Theory : real!vectors


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