Nuprl Lemma : comb_for_mset_sum_wf
λs,a,b,z. (a + b) ∈ s:DSet ⟶ a:MSet{s} ⟶ b:MSet{s} ⟶ (↓True) ⟶ MSet{s}
Proof
Definitions occuring in Statement :
mset_sum: a + b,
mset: MSet{s},
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
dset: DSet
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
mset_sum_wf,
squash_wf,
true_wf,
mset_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
Latex:
\mlambda{}s,a,b,z. (a + b) \mmember{} s:DSet {}\mrightarrow{} a:MSet\{s\} {}\mrightarrow{} b:MSet\{s\} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} MSet\{s\}
Date html generated:
2016_05_16-AM-07_46_43
Last ObjectModification:
2015_12_28-PM-06_03_36
Theory : mset
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