Nuprl Lemma : cons_functionality_wrt_permutation
∀[A:Type]. ∀L1,L2:A List. ∀x:A. (permutation(A;L1;L2) ⇒ permutation(A;[x / L1];[x / L2]))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3],
prop: ℙ,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_ind_cons_lemma,
list_ind_nil_lemma,
permutation_wf,
list_wf,
append_wf,
cons_wf,
nil_wf,
permutation_weakening,
permutation_functionality_wrt_permutation,
append_functionality_wrt_permutation
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
universeEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
productElimination
Latex:
\mforall{}[A:Type]. \mforall{}L1,L2:A List. \mforall{}x:A. (permutation(A;L1;L2) {}\mRightarrow{} permutation(A;[x / L1];[x / L2]))
Date html generated:
2016_05_14-PM-02_33_38
Last ObjectModification:
2015_12_26-PM-04_21_52
Theory : list_1
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