Nuprl Lemma : upto_is_nil
∀[n:ℕ]. uiff(upto(n) ~ [];n = 0 ∈ ℤ)
Proof
Definitions occuring in Statement :
upto: upto(n),
nil: [],
nat: ℕ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
upto: upto(n),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
le: A ≤ B
Lemmas referenced :
set_subtype_base,
le_wf,
int_subtype_base,
equal-wf-T-base,
nat_wf,
iff_weakening_uiff,
sqequal-wf-base,
from-upto-is-nil,
uiff_wf,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
decidable__le,
less_than'_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
isect_memberEquality,
isectElimination,
hypothesisEquality,
axiomEquality,
hypothesis,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
extract_by_obid,
intEquality,
lambdaEquality,
natural_numberEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
sqequalAxiom,
setElimination,
rename,
addLevel,
independent_pairFormation,
independent_functionElimination,
because_Cache,
cumulativity,
instantiate,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[n:\mBbbN{}]. uiff(upto(n) \msim{} [];n = 0)
Date html generated:
2017_04_17-AM-07_57_03
Last ObjectModification:
2017_02_27-PM-04_28_11
Theory : list_1
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