Nuprl Lemma : ideal_p_wf
∀[r:CRng]. ∀[a:|r| ⟶ ℙ]. (a Ideal of r ∈ ℙ)
Proof
Definitions occuring in Statement :
ideal_p: S Ideal of R,
crng: CRng,
rng_car: |r|,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
ideal_p: S Ideal of R,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
crng: CRng,
rng: Rng,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
infix_ap: x f y,
all: ∀x:A. B[x]
Lemmas referenced :
subgrp_p_wf,
add_grp_of_rng_wf,
all_wf,
rng_car_wf,
infix_ap_wf,
rng_times_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaEquality,
functionEquality,
applyEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
isect_memberEquality
Latex:
\mforall{}[r:CRng]. \mforall{}[a:|r| {}\mrightarrow{} \mBbbP{}]. (a Ideal of r \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_22_50
Last ObjectModification:
2015_12_27-AM-00_01_12
Theory : rings_1
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