Nuprl Lemma : one_ideal_wf
∀[r:CRng]. ((1r) ∈ Ideal(r){i})
Proof
Definitions occuring in Statement :
one_ideal: (1r),
ideal: Ideal(r){i},
crng: CRng,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
one_ideal: (1r),
ideal: Ideal(r){i},
uall: ∀[x:A]. B[x],
member: t ∈ T,
crng: CRng,
rng: Rng,
ideal_p: S Ideal of R,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
true: True,
prop: ℙ,
subgrp_p: s SubGrp of g,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t)
Lemmas referenced :
crng_wf,
true_wf,
rng_car_wf,
ideal_p_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
dependent_set_memberEquality,
lambdaEquality,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
because_Cache
Latex:
\mforall{}[r:CRng]. ((1r) \mmember{} Ideal(r)\{i\})
Date html generated:
2016_05_15-PM-00_23_05
Last ObjectModification:
2015_12_27-AM-00_01_03
Theory : rings_1
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