Nuprl Lemma : radd-list-append
∀[L1,L2:ℝ List]. (radd-list(L1 @ L2) = (radd-list(L1) + radd-list(L2)))
Proof
Definitions occuring in Statement :
req: x = y,
radd: a + b,
radd-list: radd-list(L),
real: ℝ,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
prop: ℙ,
and: P ∧ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
list_induction,
real_wf,
uall_wf,
list_wf,
req_wf,
radd-list_wf-bag,
append_wf,
list-subtype-bag,
subtype_rel_self,
radd_wf,
list_ind_nil_lemma,
radd_list_nil_lemma,
req_witness,
int-to-real_wf,
list_ind_cons_lemma,
cons_wf,
req_weakening,
req_functionality,
radd-zero-both,
req_transitivity,
radd-list-cons,
radd_functionality,
uiff_transitivity,
req_inversion,
radd-assoc,
radd-ac,
radd_comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
lambdaFormation,
rename,
productElimination
Latex:
\mforall{}[L1,L2:\mBbbR{} List]. (radd-list(L1 @ L2) = (radd-list(L1) + radd-list(L2)))
Date html generated:
2017_10_02-PM-07_15_39
Last ObjectModification:
2017_07_28-AM-07_20_35
Theory : reals
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