Nuprl Lemma : flip-conjugation1
∀[n:ℕ]. ∀[k:ℕn - 1]. ∀[j:ℕk]. ((j, k + 1) = ((k, k + 1) o ((j, k) o (k, k + 1))) ∈ (ℕn ⟶ ℕn))
Proof
Definitions occuring in Statement :
flip: (i, j),
compose: f o g,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
subtract: n - m,
add: n + m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
nat_wf,
int_seg_wf,
subtract_wf,
lelt_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_properties,
int_seg_properties,
flip-conjugation
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
productElimination,
independent_pairFormation,
hypothesis,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[k:\mBbbN{}n - 1]. \mforall{}[j:\mBbbN{}k]. ((j, k + 1) = ((k, k + 1) o ((j, k) o (k, k + 1))))
Date html generated:
2016_05_14-PM-02_13_29
Last ObjectModification:
2016_01_15-AM-07_57_05
Theory : list_1
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