Nuprl Lemma : nat-inf-infinity-new
∀[n:ℕ]. (¬(∞ = n∞ ∈ ℕ∞))
Proof
Definitions occuring in Statement :
nat-inf-infinity: ∞,
nat2inf: n∞,
nat-inf: ℕ∞,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
nat-inf: ℕ∞,
nat2inf: n∞,
nat-inf-infinity: ∞,
nat: ℕ,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
equal-wf-base-T,
nat-inf_wf,
nat2inf_wf,
nat_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_of_tt,
assert_of_lt_int,
nat_properties,
satisfiable-full-omega-tt,
intformless_wf,
itermVar_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
because_Cache,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
baseClosed,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
applyLambdaEquality,
applyEquality,
setElimination,
rename,
instantiate,
cumulativity,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
computeAll
Latex:
\mforall{}[n:\mBbbN{}]. (\mneg{}(\minfty{} = n\minfty{}))
Date html generated:
2017_10_01-AM-08_29_20
Last ObjectModification:
2017_07_26-PM-04_23_56
Theory : basic
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