Nuprl Lemma : proj-sep_antireflexive
∀[n:ℕ]. ∀[a:ℙ^n]. (¬a ≠ a)
Proof
Definitions occuring in Statement :
proj-sep: a ≠ b,
real-proj: ℙ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
proj-sep: a ≠ b,
and: P ∧ Q,
nat: ℕ,
real-vec-sep: a ≠ b,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
subtype_rel: A ⊆r B,
real: ℝ,
nat_plus: ℕ+,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
sq_stable: SqStable(P),
squash: ↓T,
guard: {T}
Lemmas referenced :
not-real-vec-sep-refl,
sq_stable__less_than,
int-to-real_wf,
real_wf,
real-vec-dist_wf,
nat_plus_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
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,
le_wf,
punit_wf,
real-vec_wf,
req_wf,
real-vec-norm_wf,
real-vec-mul_wf,
proj-sep_wf,
real-proj_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
productElimination,
extract_by_obid,
isectElimination,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
applyEquality,
lambdaEquality,
sqequalRule,
because_Cache,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
setEquality,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
minusEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a:\mBbbP{}\^{}n]. (\mneg{}a \mneq{} a)
Date html generated:
2017_10_05-AM-00_17_35
Last ObjectModification:
2017_06_18-PM-02_06_32
Theory : inner!product!spaces
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