Nuprl Lemma : imax-wf-partial-nat
∀[x,y:partial(ℕ)]. (imax(x;y) ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
partial: partial(T),
imax: imax(a;b),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
imax: imax(a;b),
has-value: (a)↓,
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
partial-base,
subtype_rel_partial,
nat_wf,
base_wf,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
subtype_rel_transitivity,
partial_wf,
set-value-type,
int-value-type,
inclusion-partial,
imax_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
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_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
is-exception_wf,
not_wf,
has-value_wf_base,
apply-2-partial,
termination,
exception-not-value,
le_int_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
bool_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
independent_isectElimination,
sqequalRule,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
hypothesisEquality,
because_Cache,
independent_pairFormation,
baseClosed,
Error :dependent_set_memberEquality_alt,
setElimination,
rename,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
Error :equalityIsType1,
productElimination,
baseApply,
closedConclusion,
applyEquality,
Error :productIsType,
callbyvalueCallbyvalue,
callbyvalueReduce,
callbyvalueExceptionCases,
imageElimination,
imageMemberEquality,
equalityElimination,
Error :equalityIsType2,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[x,y:partial(\mBbbN{})]. (imax(x;y) \mmember{} partial(\mBbbN{}))
Date html generated:
2019_06_20-PM-01_13_43
Last ObjectModification:
2018_10_07-AM-00_11_31
Theory : int_2
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