Nuprl Lemma : matom_ty_properties
∀g:GrpSig. ∀a:Atom{g}. Atomic(a)
Proof
Definitions occuring in Statement :
matom_ty: Atom{g},
matomic: Atomic(a),
all: ∀x:A. B[x],
grp_sig: GrpSig
Definitions unfolded in proof :
matomic: Atomic(a),
all: ∀x:A. B[x],
member: t ∈ T,
matom_ty: Atom{g},
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
not: ¬A,
false: False,
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T
Lemmas referenced :
squash_wf,
sq_stable__not,
mreducible_wf,
munit_wf,
not_wf,
sq_stable__and,
grp_sig_wf,
matom_ty_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
isectElimination,
isect_memberEquality,
independent_functionElimination,
introduction,
lambdaEquality,
voidElimination,
because_Cache,
productElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}g:GrpSig. \mforall{}a:Atom\{g\}. Atomic(a)
Date html generated:
2016_05_16-AM-07_44_23
Last ObjectModification:
2016_01_16-PM-11_38_01
Theory : factor_1
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