Nuprl Lemma : comb_for_omral_action_wf
λg,r,v,ps,z. (v ⋅⋅ ps) ∈ g:OCMon ⟶ r:CDRng ⟶ v:|r| ⟶ ps:|omral(g;r)| ⟶ (↓True) ⟶ |omral(g;r)|
Proof
Definitions occuring in Statement :
omral_action: v ⋅⋅ ps,
omralist: omral(g;r),
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
cdrng: CDRng,
rng_car: |r|,
ocmon: OCMon,
set_car: |p|
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
dset: DSet,
cdrng: CDRng,
crng: CRng,
rng: Rng
Lemmas referenced :
omral_action_wf,
squash_wf,
true_wf,
set_car_wf,
omralist_wf,
dset_wf,
rng_car_wf,
cdrng_wf,
ocmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
isectElimination,
applyEquality,
setElimination,
rename,
sqequalRule
Latex:
\mlambda{}g,r,v,ps,z. (v \mcdot{}\mcdot{} ps) \mmember{} g:OCMon {}\mrightarrow{} r:CDRng {}\mrightarrow{} v:|r| {}\mrightarrow{} ps:|omral(g;r)| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |omral(g;r)|
Date html generated:
2016_05_16-AM-08_26_39
Last ObjectModification:
2015_12_28-PM-06_38_07
Theory : polynom_3
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