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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