Nuprl Lemma : tswap_eval_2
∀n:ℕ. ∀i,j,k:ℕn. ((k = j ∈ ℕn) ⇒ ((swap{n}(i;j) k) = i ∈ ℕn))
Proof
Definitions occuring in Statement :
tswap: swap{n}(i;j),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
tswap: swap{n}(i;j),
all: ∀x:A. B[x],
implies: P ⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
nat: ℕ,
prop: ℙ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
swap_eval_2,
nat_wf,
int_seg_wf,
equal_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
lelt_wf,
int_seg_properties
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
dependent_set_memberEquality,
hypothesis,
equalitySymmetry,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
lambdaEquality,
setEquality,
intEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
because_Cache,
independent_functionElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j,k:\mBbbN{}n. ((k = j) {}\mRightarrow{} ((swap\{n\}(i;j) k) = i))
Date html generated:
2016_05_16-AM-07_29_52
Last ObjectModification:
2016_01_16-PM-10_06_14
Theory : perms_1
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