Nuprl Lemma : sq_stable__ideal_p
∀r:CRng. ∀a:|r| ⟶ ℙ. ((∀x:|r|. SqStable(a x)) ⇒ SqStable(a Ideal of r))
Proof
Definitions occuring in Statement :
ideal_p: S Ideal of R,
crng: CRng,
rng_car: |r|,
sq_stable: SqStable(P),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
ideal_p: S Ideal of R,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
crng: CRng,
rng: Rng,
add_grp_of_rng: r↓+gp,
grp_car: |g|,
pi1: fst(t),
so_lambda: λ2x.t[x],
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s],
subgrp_p: s SubGrp of g,
and: P ∧ Q,
infix_ap: x f y
Lemmas referenced :
sq_stable__and,
subgrp_p_wf,
add_grp_of_rng_wf,
all_wf,
rng_car_wf,
infix_ap_wf,
rng_times_wf,
grp_id_wf,
grp_car_wf,
grp_inv_wf,
grp_op_wf,
sq_stable__all,
sq_stable_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isect_memberEquality,
lambdaEquality,
because_Cache,
functionEquality,
applyEquality,
universeEquality,
independent_functionElimination,
productEquality,
dependent_functionElimination,
cumulativity
Latex:
\mforall{}r:CRng. \mforall{}a:|r| {}\mrightarrow{} \mBbbP{}. ((\mforall{}x:|r|. SqStable(a x)) {}\mRightarrow{} SqStable(a Ideal of r))
Date html generated:
2016_05_15-PM-00_22_52
Last ObjectModification:
2015_12_27-AM-00_01_18
Theory : rings_1
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