Nuprl Lemma : DCC-order-type-less
DCC(WFO{i:l}();order-type-less())
Proof
Definitions occuring in Statement :
WFO: WFO{i:l}(),
order-type-less: order-type-less(),
DCC: DCC(T;<)
Definitions unfolded in proof :
WFO: WFO{i:l}(),
DCC: DCC(T;<),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
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,
top: Top,
and: P ∧ Q,
order-type-less: order-type-less(),
infix_ap: x f y,
spreadn: spread3,
pi1: fst(t),
pi2: snd(t),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
order-preserving: order-preserving(A;B;a1,a2.R1[a1; a2];b1,b2.R2[b1; b2];f),
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than': less_than'(a;b),
le: A ≤ B,
istype: istype(T),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
bfalse: ff,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
compose: f o g,
subtract: n - m,
lelt: i ≤ j < k,
int_seg: {i..j-}
Lemmas referenced :
istype-nat,
infix_ap_wf,
DCC_wf,
order-type-less_wf,
subtype_rel_self,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
istype-universe,
order-preserving_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
nat_wf,
subtract-1-ge-0,
primrec0_lemma,
less_than_wf,
ge_wf,
int_formula_prop_less_lemma,
intformless_wf,
le_wf,
istype-false,
subtype_rel-equal,
subtype_rel_dep_function,
int_term_value_subtract_lemma,
itermSubtract_wf,
compose_wf,
assert_wf,
iff_weakening_uiff,
assert-bnot,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases_sqequal,
int_subtype_base,
eqff_to_assert,
assert_of_lt_int,
eqtt_to_assert,
lt_int_wf,
primrec-unroll,
add-subtract-cancel,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
istype-less_than,
pi2_wf,
complete-nat-induction-ext,
all_wf,
subtract-add-cancel,
zero-add,
add-commutes,
add-swap,
add-associates,
decidable__lt,
subtract_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
bnot_wf,
le_int_wf,
set_subtype_base,
equal-wf-base,
uiff_transitivity,
int_seg_wf,
int_seg_subtype_nat,
int_seg_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalRule,
functionIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
universeIsType,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
closedConclusion,
productEquality,
cumulativity,
universeEquality,
functionEquality,
hypothesisEquality,
because_Cache,
applyEquality,
dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
productIsType,
inhabitedIsType,
productElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
functionExtensionality,
functionIsTypeImplies,
axiomEquality,
intWeakElimination,
equalityIsType1,
baseClosed,
baseApply,
equalityIsType2,
equalityElimination,
intEquality,
independent_pairEquality
Latex:
DCC(WFO\{i:l\}();order-type-less())
Date html generated:
2019_10_15-AM-11_10_48
Last ObjectModification:
2018_12_08-PM-04_28_04
Theory : general
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