Nuprl Lemma : cons_cons_permr
∀T:Type. ∀a,a':T. ∀as,as':T List. ((as ≡(T) as') ⇒ ([a; [a' / as]] ≡(T) [a'; [a / as']]))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
cons: [a / b],
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
permr_functionality_wrt_permr,
cons_wf,
permr_weakening,
cons_functionality_wrt_permr,
permr_inversion,
hd_two_swap_permr,
permr_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
isectElimination,
hypothesis,
independent_functionElimination,
productElimination,
universeIsType,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}a,a':T. \mforall{}as,as':T List. ((as \mequiv{}(T) as') {}\mRightarrow{} ([a; [a' / as]] \mequiv{}(T) [a'; [a / as']]))
Date html generated:
2020_05_20-AM-09_35_28
Last ObjectModification:
2020_01_08-PM-06_00_20
Theory : perms_2
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