Nuprl Lemma : map_map
∀[f,g,a:Top]. (map(g;map(f;a)) ~ map(g o f;a))
Proof
Definitions occuring in Statement :
map: map(f;as),
compose: f o g,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
guard: {T},
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
top: Top,
compose: f o g
Lemmas referenced :
top_wf,
map_nil_lemma,
sqle_wf_base,
map_cons_lemma,
is-exception_wf,
base_wf,
has-value_wf_base,
sqequal-list_ind
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueCallbyvalue,
hypothesis,
callbyvalueReduce,
callbyvalueExceptionCases,
inlFormation,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inrFormation,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
divergentSqle,
sqleRule,
sqleReflexivity,
because_Cache,
sqequalAxiom
Latex:
\mforall{}[f,g,a:Top]. (map(g;map(f;a)) \msim{} map(g o f;a))
Date html generated:
2016_05_14-AM-06_54_35
Last ObjectModification:
2016_01_14-PM-08_15_39
Theory : list_0
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