Nuprl Lemma : fabgrp_umap_wf
∀s:DSet. ∀f:fabgrp_sig{i:l}(s). (f.umap ∈ grp':AbGrp ⟶ (|s| ⟶ |grp'|) ⟶ |f.grp| ⟶ |grp'|)
Proof
Definitions occuring in Statement :
fabgrp_umap: f.umap,
fabgrp_grp: f.grp,
fabgrp_sig: fabgrp_sig{i:l}(s),
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
abgrp: AbGrp,
grp_car: |g|,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
fabgrp_sig: fabgrp_sig{i:l}(s),
fabgrp_umap: f.umap,
fabgrp_grp: f.grp,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
fabgrp_sig_wf,
dset_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:DSet. \mforall{}f:fabgrp\_sig\{i:l\}(s). (f.umap \mmember{} grp':AbGrp {}\mrightarrow{} (|s| {}\mrightarrow{} |grp'|) {}\mrightarrow{} |f.grp| {}\mrightarrow{} |grp'|)
Date html generated:
2016_05_16-AM-08_13_30
Last ObjectModification:
2015_12_28-PM-06_09_43
Theory : polynom_1
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