Nuprl Lemma : compat-cons
∀[T:Type]. ∀as,bs:T List. ∀a,b:T. ([a / as] || [b / bs] ⇐⇒ (a = b ∈ T) ∧ as || bs)
Proof
Definitions occuring in Statement :
compat: l1 || l2,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
compat: l1 || l2,
or: P ∨ Q,
guard: {T},
cand: A c∧ B
Lemmas referenced :
compat_wf,
cons_wf,
and_wf,
equal_wf,
list_wf,
cons_iseg,
iseg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
universeEquality,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
equalitySymmetry,
inlFormation,
sqequalRule,
inrFormation
Latex:
\mforall{}[T:Type]. \mforall{}as,bs:T List. \mforall{}a,b:T. ([a / as] || [b / bs] \mLeftarrow{}{}\mRightarrow{} (a = b) \mwedge{} as || bs)
Date html generated:
2016_05_15-PM-03_49_52
Last ObjectModification:
2015_12_27-PM-01_22_25
Theory : general
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