Nuprl Lemma : fma_inj_wf
∀G:GrpSig. ∀A:RngSig. ∀f:fma_sig{i:l}(G;A). (f.inj ∈ |G| ⟶ f.alg.car)
Proof
Definitions occuring in Statement :
fma_inj: f.inj,
fma_alg: f.alg,
fma_sig: fma_sig{i:l}(G;A),
alg_car: a.car,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
rng_sig: RngSig,
grp_car: |g|,
grp_sig: GrpSig
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
fma_sig: fma_sig{i:l}(G;A),
fma_inj: f.inj,
fma_alg: f.alg,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
fma_sig_wf,
rng_sig_wf,
grp_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{}G:GrpSig. \mforall{}A:RngSig. \mforall{}f:fma\_sig\{i:l\}(G;A). (f.inj \mmember{} |G| {}\mrightarrow{} f.alg.car)
Date html generated:
2016_05_16-AM-08_14_17
Last ObjectModification:
2015_12_28-PM-06_09_21
Theory : polynom_1
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