Nuprl Lemma : rng_lsum_wf
∀r:Rng. ∀A:Type. ∀as:A List. ∀f:A ⟶ |r|. (Σ{A,r} x ∈ as. f[x] ∈ |r|)
Proof
Definitions occuring in Statement :
rng_lsum: Σ{A,r} x ∈ as. f[x],
list: T List,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
rng: Rng,
rng_car: |r|
Definitions unfolded in proof :
rng_lsum: Σ{A,r} x ∈ as. f[x],
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
grp: Group{i},
mon: Mon,
imon: IMonoid,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
rng: Rng
Lemmas referenced :
mon_for_wf,
add_grp_of_rng_wf_a,
grp_sig_wf,
monoid_p_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
inverse_wf,
grp_inv_wf,
rng_car_wf,
add_grp_of_rng_wf,
list_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
cumulativity,
functionEquality,
universeEquality
Latex:
\mforall{}r:Rng. \mforall{}A:Type. \mforall{}as:A List. \mforall{}f:A {}\mrightarrow{} |r|. (\mSigma{}\{A,r\} x \mmember{} as. f[x] \mmember{} |r|)
Date html generated:
2016_05_16-AM-08_11_41
Last ObjectModification:
2015_12_28-PM-06_06_19
Theory : list_3
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