Nuprl Lemma : nat2inf_wf
∀[n:ℕ]. (n∞ ∈ ℕ∞)
Proof
Definitions occuring in Statement :
nat2inf: n∞,
nat-inf: ℕ∞,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
nat-inf: ℕ∞,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat2inf: n∞,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
so_apply: x[s]
Lemmas referenced :
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
all_wf,
assert_wf,
assert_of_lt_int,
nat_wf,
lt_int_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaFormation,
productElimination,
independent_isectElimination,
addEquality,
natural_numberEquality,
functionEquality,
applyEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. (n\minfty{} \mmember{} \mBbbN{}\minfty{})
Date html generated:
2016_05_15-PM-01_46_50
Last ObjectModification:
2016_01_15-PM-11_17_15
Theory : basic
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