Nuprl Lemma : gcopower_inj_wf
∀s:PosetSig. ∀g:GrpSig. ∀g1:gcopower_sig{i:l}(s;g). (g1.inj ∈ |s| ⟶ |g| ⟶ |g1.grp|)
Proof
Definitions occuring in Statement :
gcopower_inj: g1.inj,
gcopower_grp: g1.grp,
gcopower_sig: gcopower_sig{i:l}(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
grp_car: |g|,
grp_sig: GrpSig,
set_car: |p|,
poset_sig: PosetSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
gcopower_sig: gcopower_sig{i:l}(s;g),
gcopower_inj: g1.inj,
gcopower_grp: g1.grp,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
gcopower_sig_wf,
grp_sig_wf,
poset_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesisEquality,
hypothesis,
lemma_by_obid,
dependent_functionElimination
Latex:
\mforall{}s:PosetSig. \mforall{}g:GrpSig. \mforall{}g1:gcopower\_sig\{i:l\}(s;g). (g1.inj \mmember{} |s| {}\mrightarrow{} |g| {}\mrightarrow{} |g1.grp|)
Date html generated:
2016_05_16-AM-08_13_43
Last ObjectModification:
2015_12_28-PM-06_09_27
Theory : polynom_1
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