Nuprl Lemma : permutation-swap-first2
∀[A:Type]. ∀x,y:A. ∀L:A List. permutation(A;[x; [y / L]];[y; [x / L]])
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],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
cand: A c∧ B,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
permutation-cons,
cons_wf,
nil_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
permutation_weakening,
and_wf,
equal_wf,
list_wf,
permutation_wf,
exists_wf,
append_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
dependent_pairFormation,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
independent_isectElimination,
lambdaEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}x,y:A. \mforall{}L:A List. permutation(A;[x; [y / L]];[y; [x / L]])
Date html generated:
2016_05_14-PM-02_32_02
Last ObjectModification:
2015_12_26-PM-04_22_47
Theory : list_1
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