Nuprl Lemma : rotate-by-injection
∀[n,i:ℕ]. Inj(ℕn;ℕn;rotate-by(n;i))
Proof
Definitions occuring in Statement :
rotate-by: rotate-by(n;i),
inject: Inj(A;B;f),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
nat: ℕ,
prop: ℙ,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
int_seg_wf,
rotate-by_wf,
nat_wf,
inject_wf,
squash_wf,
true_wf,
iterate-rotate-rotate-by,
iff_weakening_equal,
fun_exp-injection,
rotate_wf,
rotate-injection
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
axiomEquality,
hypothesis,
extract_by_obid,
isectElimination,
natural_numberEquality,
setElimination,
rename,
applyEquality,
isect_memberEquality,
because_Cache,
imageElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[n,i:\mBbbN{}]. Inj(\mBbbN{}n;\mBbbN{}n;rotate-by(n;i))
Date html generated:
2018_05_21-PM-08_19_13
Last ObjectModification:
2017_07_26-PM-05_52_41
Theory : general
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