Nuprl Lemma : drng_subtype_rng
DRng ⊆r Rng
Proof
Definitions occuring in Statement :
drng: DRng,
rng: Rng,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
drng: DRng,
rng: Rng,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B
Lemmas referenced :
subtype_rel_sets,
rng_sig_wf,
and_wf,
ring_p_wf,
rng_car_wf,
rng_plus_wf,
rng_zero_wf,
rng_minus_wf,
rng_times_wf,
rng_one_wf,
eqfun_p_wf,
rng_eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
lambdaEquality,
cumulativity,
hypothesisEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
productElimination
Latex:
DRng \msubseteq{}r Rng
Date html generated:
2016_05_15-PM-00_20_29
Last ObjectModification:
2015_12_27-AM-00_02_53
Theory : rings_1
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