Nuprl Lemma : posint_well_fnd
WellFnd{i}(|<ℤ+,*>|;x,y.x p| y)
Proof
Definitions occuring in Statement :
posint_mul_mon: <ℤ+,*>,
mpdivides: a p| b,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
grp_car: |g|
Definitions unfolded in proof :
mpdivides: a p| b,
mdivides: b | a,
posint_mul_mon: <ℤ+,*>,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
infix_ap: x f y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
so_apply: x[s1;s2],
nat_plus: ℕ+,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
subtype_rel: A ⊆r B,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
int_seg: {i..j-},
lelt: i ≤ j < k,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
nat: ℕ,
uiff: uiff(P;Q),
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
ge: i ≥ j
Lemmas referenced :
wellfounded_functionality_wrt_iff,
nat_plus_wf,
exists_wf,
equal_wf,
mul_nat_plus,
not_wf,
divides_wf,
divides_nchar,
not_functionality_wrt_iff,
pdivisor_bound,
nat_plus_subtype_nat,
wellfounded_functionality_wrt_implies,
less_than_wf,
all_wf,
int_seg_properties,
nat_plus_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
decidable__equal_int,
subtract_wf,
subtype_base_sq,
set_subtype_base,
lelt_wf,
int_subtype_base,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
decidable__le,
decidable__lt,
subtype_rel_self,
le_wf,
false_wf,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
set_wf,
primrec-wf2,
nat_wf,
nat_properties,
itermAdd_wf,
int_term_value_add_lemma,
subtract-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
lambdaEquality,
productEquality,
hypothesisEquality,
setElimination,
rename,
independent_isectElimination,
independent_functionElimination,
lambdaFormation,
independent_pairFormation,
productElimination,
dependent_functionElimination,
promote_hyp,
applyEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberFormation,
functionEquality,
cumulativity,
universeEquality,
natural_numberEquality,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
unionElimination,
instantiate,
applyLambdaEquality,
dependent_set_memberEquality,
hypothesis_subsumption,
addEquality,
minusEquality
Latex:
WellFnd\{i\}(|<\mBbbZ{}\msupplus{},*>|;x,y.x p| y)
Date html generated:
2019_10_16-PM-01_06_05
Last ObjectModification:
2018_09_17-PM-06_16_15
Theory : factor_1
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