Nuprl Lemma : rev_permf_wf
∀n:ℕ. (rev_permf(n) ∈ ℕn ⟶ ℕn)
Proof
Definitions occuring in Statement :
rev_permf: rev_permf(n),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
rev_permf: rev_permf(n),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
nat: ℕ,
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ
Lemmas referenced :
subtract_wf,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
decidable__lt,
lelt_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lambdaEquality,
dependent_set_memberEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
natural_numberEquality,
hypothesisEquality,
independent_pairFormation,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}n:\mBbbN{}. (rev\_permf(n) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbN{}n)
Date html generated:
2018_05_22-AM-07_44_33
Last ObjectModification:
2018_05_19-AM-08_33_20
Theory : perms_1
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