Nuprl Lemma : permr_functionality_wrt_permr
∀T,T':Type. ∀as:T List. ∀as':T' List. ∀bs:T List. ∀bs':T' List.
((T = T' ∈ Type) ⇒ (as ≡(T) as') ⇒ (bs ≡(T) bs') ⇒ (as ≡(T) bs ⇐⇒ as' ≡(T') bs'))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
list: T List,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
squash: ↓T,
true: True,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
permr_wf,
subtype_rel_self,
list_wf,
subtype_rel_wf,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
permr_inversion,
permr_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
equalitySymmetry,
isectElimination,
hyp_replacement,
applyLambdaEquality,
sqequalRule,
instantiate,
universeEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache
Latex:
\mforall{}T,T':Type. \mforall{}as:T List. \mforall{}as':T' List. \mforall{}bs:T List. \mforall{}bs':T' List.
((T = T') {}\mRightarrow{} (as \mequiv{}(T) as') {}\mRightarrow{} (bs \mequiv{}(T) bs') {}\mRightarrow{} (as \mequiv{}(T) bs \mLeftarrow{}{}\mRightarrow{} as' \mequiv{}(T') bs'))
Date html generated:
2017_01_09-AM-08_35_14
Last ObjectModification:
2016_07_12-PM-01_10_23
Theory : perms_2
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