Nuprl Lemma : tl_perm_wf
∀n:ℕ+. ∀p:Perm(ℕn). (tl_perm(p) ∈ Perm(ℕ+n))
Proof
Definitions occuring in Statement :
tl_perm: tl_perm(p),
perm: Perm(T),
int_seg: {i..j-},
nat_plus: ℕ+,
all: ∀x:A. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
perm: Perm(T),
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
tl_perm: tl_perm(p),
comp_perm: comp_perm,
txpose_perm: txpose_perm,
mk_perm: mk_perm(f;b),
perm_f: p.f,
pi1: fst(t),
compose: f o g,
swap: swap(i;j),
int_seg: {i..j-},
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 ,
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B,
decidable: Dec(P),
nequal: a ≠ b ∈ T ,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
rev_implies: P ⇐ Q,
pi2: snd(t),
perm_b: p.b,
true: True,
sym_grp: Sym(n),
inv_funs: InvFuns(A;B;f;g),
identity: Id,
tidentity: Id{T}
Lemmas referenced :
perm_wf,
int_seg_wf,
nat_plus_wf,
mk_perm_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
int_seg_properties,
nat_plus_properties,
full-omega-unsat,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
less_than_wf,
le_wf,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
intformless_wf,
intformnot_wf,
decidable__lt,
istype-false,
perm_b_wf,
perm_b_to_f,
decidable__le,
decidable__equal_int,
int_subtype_base,
lelt_wf,
set_subtype_base,
perm_f_wf,
perm_f_inj,
equal-wf-T-base,
equal-wf-base-T,
iff_transitivity,
iff_weakening_uiff,
equal_symmetry,
equal_wf,
not_wf,
bnot_wf,
assert_wf,
uiff_transitivity,
assert_of_bnot,
iff_weakening_equal,
subtype_rel_self,
istype-universe,
true_wf,
squash_wf,
perm_b_inj,
equal-wf-base,
le_weakening2,
nat_plus_subtype_nat,
txpose_perm_wf,
comp_perm_wf,
perm_b_f_cancel,
perm_f_b_cancel,
inv_funs_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
dependent_set_memberEquality_alt,
sqequalHypSubstitution,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
imageElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
because_Cache,
equalityIsType1,
productIsType,
applyEquality,
applyLambdaEquality,
baseClosed,
intEquality,
equalityIsType4,
closedConclusion,
baseApply,
imageMemberEquality,
universeEquality
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. \mforall{}p:Perm(\mBbbN{}n). (tl\_perm(p) \mmember{} Perm(\mBbbN{}\msupplus{}n))
Date html generated:
2019_10_16-PM-01_00_49
Last ObjectModification:
2019_06_20-PM-06_44_18
Theory : perms_2
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