Nuprl Lemma : extend_permf_wf
∀n:ℕ. ∀p:ℕn ⟶ ℕn. (extend_permf(p;n) ∈ ℕn + 1 ⟶ ℕn + 1)
Proof
Definitions occuring in Statement :
extend_permf: extend_permf(pf;n),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
extend_permf: extend_permf(pf;n),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
lelt: i ≤ j < k,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
true: True
Lemmas referenced :
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
int_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nat_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
intformeq_wf,
itermAdd_wf,
itermConstant_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
le_wf,
less_than_wf,
int_seg_subtype,
istype-false,
decidable__le,
not-le-2,
not-equal-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-mul-special,
zero-mul,
add-zero,
add-associates,
add-commutes,
le-add-cancel,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
lambdaEquality_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
because_Cache,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
inhabitedIsType,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation_alt,
equalityIsType2,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
dependent_set_memberEquality_alt,
independent_pairFormation,
natural_numberEquality,
approximateComputation,
int_eqEquality,
isect_memberEquality_alt,
universeIsType,
productIsType,
addEquality,
minusEquality,
multiplyEquality,
equalityIsType1,
functionIsType
Latex:
\mforall{}n:\mBbbN{}. \mforall{}p:\mBbbN{}n {}\mrightarrow{} \mBbbN{}n. (extend\_permf(p;n) \mmember{} \mBbbN{}n + 1 {}\mrightarrow{} \mBbbN{}n + 1)
Date html generated:
2019_10_16-PM-00_59_48
Last ObjectModification:
2018_10_08-AM-09_20_24
Theory : perms_1
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