Nuprl Lemma : map_functionality
∀A,B:Type. ∀f,f':A ⟶ B. ∀as,as':A List. ((f = f' ∈ (A ⟶ B)) ⇒ (as ≡(A) as') ⇒ (map(f;as) ≡(B) map(f';as')))
Proof
Definitions occuring in Statement :
permr: as ≡(T) bs,
map: map(f;as),
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
permr_wf,
list_wf,
istype-universe,
map_wf,
map_permr_func,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
equalityIsType1,
inhabitedIsType,
isectElimination,
functionIsType,
universeEquality,
natural_numberEquality,
because_Cache,
independent_functionElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination
Latex:
\mforall{}A,B:Type. \mforall{}f,f':A {}\mrightarrow{} B. \mforall{}as,as':A List.
((f = f') {}\mRightarrow{} (as \mequiv{}(A) as') {}\mRightarrow{} (map(f;as) \mequiv{}(B) map(f';as')))
Date html generated:
2019_10_16-PM-01_02_31
Last ObjectModification:
2018_10_08-AM-11_32_52
Theory : list_2
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