Nuprl Lemma : mprime_wf
∀g:GrpSig. ∀a:|g|. (IsPrime(a) ∈ ℙ)
Proof
Definitions occuring in Statement :
mprime: IsPrime(a),
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
grp_car: |g|,
grp_sig: GrpSig
Definitions unfolded in proof :
mprime: IsPrime(a),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
infix_ap: x f y,
so_apply: x[s]
Lemmas referenced :
and_wf,
not_wf,
munit_wf,
all_wf,
grp_car_wf,
mdivides_wf,
grp_op_wf,
or_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
applyEquality
Latex:
\mforall{}g:GrpSig. \mforall{}a:|g|. (IsPrime(a) \mmember{} \mBbbP{})
Date html generated:
2016_05_16-AM-07_43_52
Last ObjectModification:
2015_12_28-PM-05_54_17
Theory : factor_1
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