Nuprl Lemma : comb_for_rng_mssum_wf
λs,r,f,a,z. Σx ∈ a. f[x] ∈ s:DSet ⟶ r:Rng ⟶ f:(|s| ⟶ |r|) ⟶ a:MSet{s} ⟶ (↓True) ⟶ |r|
Proof
Definitions occuring in Statement :
rng_mssum: rng_mssum,
mset: MSet{s},
so_apply: x[s],
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
rng: Rng,
rng_car: |r|,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
dset: DSet,
rng: Rng
Lemmas referenced :
rng_mssum_wf,
squash_wf,
true_wf,
mset_wf,
set_car_wf,
rng_car_wf,
rng_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
isectElimination,
functionEquality,
setElimination,
rename
Latex:
\mlambda{}s,r,f,a,z. \mSigma{}x \mmember{} a. f[x] \mmember{} s:DSet {}\mrightarrow{} r:Rng {}\mrightarrow{} f:(|s| {}\mrightarrow{} |r|) {}\mrightarrow{} a:MSet\{s\} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |r|
Date html generated:
2016_05_16-AM-08_11_50
Last ObjectModification:
2015_12_28-PM-06_06_13
Theory : list_3
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