Nuprl Lemma : swap_wf
∀n:ℕ. ∀i,j:ℕn. (swap(i;j) ∈ ℕn ⟶ ℕn)
Proof
Definitions occuring in Statement :
swap: swap(i;j),
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,
swap: swap(i;j),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
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 ,
bfalse: ff,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nat: ℕ
Lemmas referenced :
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
int_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
lambdaEquality_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
because_Cache,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
inhabitedIsType,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation_alt,
equalityIsType2,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
equalityIsType1,
universeIsType,
natural_numberEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}i,j:\mBbbN{}n. (swap(i;j) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbN{}n)
Date html generated:
2019_10_16-PM-00_59_09
Last ObjectModification:
2018_10_08-AM-09_28_26
Theory : perms_1
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