Nuprl Lemma : map_append_sq
∀[f,a,b:Top]. (map(f;a @ b) ~ map(f;a) @ map(f;b))
Proof
Definitions occuring in Statement :
map: map(f;as),
append: as @ bs,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
append: as @ bs,
map: map(f;as),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
strict1: strict1(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
list_ind: list_ind,
has-value: (a)↓,
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
top: Top
Lemmas referenced :
sqequal-list_ind,
has-value_wf_base,
istype-base,
is-exception_wf,
map_cons_lemma,
istype-void,
list_ind_cons_lemma,
istype-sqle,
list_ind_nil_lemma,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_isectElimination,
independent_pairFormation,
Error :lambdaFormation_alt,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
Error :universeIsType,
callbyvalueExceptionCases,
Error :inlFormation_alt,
imageMemberEquality,
imageElimination,
exceptionSqequal,
Error :inrFormation_alt,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
divergentSqle,
sqleRule,
sqleReflexivity,
Error :inhabitedIsType,
because_Cache,
axiomSqEquality,
Error :isectIsTypeImplies
Latex:
\mforall{}[f,a,b:Top]. (map(f;a @ b) \msim{} map(f;a) @ map(f;b))
Date html generated:
2019_06_20-PM-00_39_39
Last ObjectModification:
2019_01_03-AM-09_48_06
Theory : list_0
Home
Index