Nuprl Lemma : nat-inf-infinity_wf
∞ ∈ ℕ∞
Proof
Definitions occuring in Statement :
nat-inf-infinity: ∞,
nat-inf: ℕ∞,
member: t ∈ T
Definitions unfolded in proof :
nat-inf-infinity: ∞,
all: ∀x:A. B[x],
implies: P ⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
nat: ℕ,
subtype_rel: A ⊆r B,
top: Top,
nat-inf: ℕ∞,
so_lambda: λ2x.t[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
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,
nat_wf,
top_wf,
btrue_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lambdaFormation,
hypothesis,
natural_numberEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
lambdaEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
intEquality,
dependent_set_memberEquality,
functionEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
because_Cache
Latex:
\minfty{} \mmember{} \mBbbN{}\minfty{}
Date html generated:
2016_05_15-PM-01_46_58
Last ObjectModification:
2016_01_15-PM-11_17_12
Theory : basic
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