Nuprl Lemma : alg_p_wf
∀r:RngSig. ∀a:algebra_sig{i:l}(|r|). (AlgP(r;a) ∈ ℙ)
Proof
Definitions occuring in Statement :
alg_p: AlgP(r;a),
algebra_sig: algebra_sig{i:l}(A),
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
rng_car: |r|,
rng_sig: RngSig
Definitions unfolded in proof :
alg_p: AlgP(r;a),
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rng_p_wf,
rng_of_alg_wf,
rng_car_wf,
action_p_wf,
rng_times_wf,
rng_one_wf,
alg_car_wf,
alg_act_wf,
bilinear_p_wf,
rng_plus_wf,
alg_plus_wf,
all_wf,
dist_1op_2op_lr_wf,
alg_times_wf,
algebra_sig_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaEquality,
applyEquality
Latex:
\mforall{}r:RngSig. \mforall{}a:algebra\_sig\{i:l\}(|r|). (AlgP(r;a) \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-08_13_59
Last ObjectModification:
2015_12_28-PM-06_09_36
Theory : polynom_1
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