Nuprl Lemma : rotate-surjection
∀n:ℕ+. Surj(ℕn;ℕn;rot(n))
Proof
Definitions occuring in Statement :
rotate: rot(n),
surject: Surj(A;B;f),
int_seg: {i..j-},
nat_plus: ℕ+,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
prop: ℙ,
top: Top,
not: ¬A,
implies: P ⇒ Q,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
guard: {T},
nat: ℕ,
exists: ∃x:A. B[x],
compose: f o g,
nat_plus: ℕ+,
surject: Surj(A;B;f),
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
equal_wf,
nat_plus_subtype_nat,
rotate_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_plus_properties,
int_seg_properties,
subtract_wf,
fun_exp_wf,
int_seg_wf,
nat_plus_wf,
rotate-inverse1
Rules used in proof :
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
productElimination,
equalitySymmetry,
equalityTransitivity,
dependent_set_memberEquality,
because_Cache,
dependent_pairFormation,
sqequalRule,
functionExtensionality,
applyEquality,
applyLambdaEquality,
rename,
setElimination,
natural_numberEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. Surj(\mBbbN{}n;\mBbbN{}n;rot(n))
Date html generated:
2017_04_17-AM-08_09_03
Last ObjectModification:
2017_03_29-PM-00_35_31
Theory : list_1
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