Nuprl Lemma : rng_div_wf
∀[r:RngSig]. (÷r ∈ |r| ⟶ |r| ⟶ (|r|?))
Proof
Definitions occuring in Statement :
rng_div: ÷r,
rng_car: |r|,
rng_sig: RngSig,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rng_sig: RngSig,
rng_div: ÷r,
rng_car: |r|,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid
Latex:
\mforall{}[r:RngSig]. (\mdiv{}r \mmember{} |r| {}\mrightarrow{} |r| {}\mrightarrow{} (|r|?))
Date html generated:
2016_05_15-PM-00_20_18
Last ObjectModification:
2015_12_27-AM-00_03_00
Theory : rings_1
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