Nuprl Lemma : comb_for_mset_inj_wf
λs,x,z. mset_inj{s}(x) ∈ s:DSet ⟶ x:|s| ⟶ (↓True) ⟶ MSet{s}
Proof
Definitions occuring in Statement :
mset_inj: mset_inj{s}(x),
mset: MSet{s},
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
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
Lemmas referenced :
mset_inj_wf,
squash_wf,
true_wf,
set_car_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,
setElimination,
rename
Latex:
\mlambda{}s,x,z. mset\_inj\{s\}(x) \mmember{} s:DSet {}\mrightarrow{} x:|s| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} MSet\{s\}
Date html generated:
2016_05_16-AM-07_46_38
Last ObjectModification:
2015_12_28-PM-06_03_44
Theory : mset
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