Nuprl Lemma : permutation-cons2
∀[A:Type]. ∀x:A. ∀L1,L2:A List. (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,
member: t ∈ T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
append: as @ bs,
list_ind: list_ind,
nil: [],
it: ⋅,
cons: [a / b],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
permutation_wf,
list_wf,
permutation-cons,
cons_wf,
nil_wf,
and_wf,
equal_wf,
append_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination,
dependent_pairFormation,
sqequalRule,
because_Cache,
independent_pairFormation,
lambdaEquality
Latex:
\mforall{}[A:Type]. \mforall{}x:A. \mforall{}L1,L2:A List. (permutation(A;L1;L2) {}\mRightarrow{} permutation(A;[x / L1];[x / L2]))
Date html generated:
2016_05_14-PM-02_31_53
Last ObjectModification:
2015_12_26-PM-04_22_55
Theory : list_1
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